Is it generally safe to walk through a field of cows?

Depends very heavily on the cows. Cattle rancher here. Be careful about it and most cattle are OK to walk among.
Generally speaking, most farm cattle are timid towards people. They may come check you out and encircle you as a herd, but will usually scurry away if you move suddenly, and don't care if you're just in the field with them. They are herbivorous herd/prey animals, after all. The cattle my parents raise, perfectly safe to walk through. Hell the calves will often come up and sniff you out and rub up against you.
Some remote range cattle can be more wild. They might take off running if they see you within a half mile, or they might come running towards you if they deem you a threat.
The real danger often lies with bulls (hanging balls and huge shoulder) or cows with young calves (<1mo old). Both of these can be very unpredictable.
I've interacted with some bulls that were as gentle as can be and some that would rip your skin off if you weren't on the other side of a panel. You should never go into a paddock with an unknown bull, ever.
And even the most timid cow can start squaring up if she has a very young calf still in need of protection.
It's something you mostly have to learn how to read. Cows are expressive. They have body language. They speak with their head and their tails, and they look with their ears. For me it's easy to tell if a cow is safe to approach, but it is a learned skill.
When you approach cows, make noise. Nothing racocious but just talking in a firm tone to them is enough. Make sure the herd olknows your approaching long before you get close enough to be a danger, never suprise a cow. Always keep a distance of minimum 30 feet unless they approach you themselves out of curiosity.
A head and/or tail held very high means they are alert and focused on you, this usually means they are nervous and about to fight-or-flight. Back off slowly and try not to turn away.
If a herd dispersed while grazing begins to bunch up together, that also means they're getting nervous. Just avoid the bunch and walk away from whatever direction they're heading.
A head held low while looking at you, or still grazing means they are relaxed. They dont usually lower their head to "charge" like in the cartoons until they're already moving. You're new to the field so they'll always look at you. Move smoothly and steadily, they won't bother you.
- Me as a kid: running away from a curious cow
  The cow, running behind me: "wait, I want to check you out! What are we running away from anyways?"
  
  Haha yeah they'll do that. They can be insufferably curious.
  I remember one time one of our border collie pups (not old enough to work but just getting introduced to the herd) got away from my mom. The cows all came over to check her out and she took off with the whole herd right after her!
  She wasn't that interested in working much after that...
- If OP walks there frequently then he could also start to befriend them. Offer them some grass, give them some pets & head scratches. Cows are pretty social and usually friendly animals. So if you're nice to them, they'll be nice to you too, but most importantly learn that you're no threat to them.
  
  Fun fact, cow licks feel like being rubbed by low-grade sandpaper.
- I love this post. Thanks for sharing all that!

Yes. They might follow you, but that's mostly out of curiosity and the fact that you're tall enough to be their leader. Sometimes they might even run at you, but that's mostly just to catch up and/or get closer - They're not charging at you. Stop, turn around, and T-pose, and they'll stop as well, waiting to see what you're up to.
Cows alone are pretty chill and playful. Think of them like huge dogs, but without the instinct for hunting. If there are young ones with them you wanna give them some extra space for obvious reasons.
Source: Grew up on a cattle farm.
- Cows are big, strong and heavy, and docile dogs can also kill. Any kind of caution around things large or feisty enough to kill you is healthy.
- Glad to hear t-pose is the way to go. I'm beginning to think it's the solution to the world's problems.

Paraglider pilot here, so I landed among the cow my fair share of times.
Cows are curious but shy, if you walk slowly they might come to have a look, if they get too close, something like clapping your hands is enough to have them running away. However, if the farmer didn't took the veals the yet, they can be pretty agressive to protect their kids, in that case forgot what I said about "clapping your hand" and stay away from the herd. Note also that bull are less shy than cow.
- "The veals"
  I think they're called calf's until they leave the abattoir.
- bull are less shy
  That's right; I have to hype myself up to get in the right mindset though.

From my understanding, you are pretty safe as long as you don't provoke them (walking through the middle of them might be considered provoking) or near their calves. This article from the UK states "Where recorded, 91% of HSE reported fatalities on the public were caused by cows with calves". Basically, mothers with a child are going to be very protective.
Cows are a domesticated creature, so they are generally docile, but I would exercise caution because if need be they will use their mass and strength against you. I've heard of stories of farmers running from cows and narrowly escaping under a fence. Most of these did involve a farmer trying to separate a calve from it's mother. I've also heard stories of cows jumping fences.
And as far as memes go:

Country boy here - cows are pretty harmless most of the time if you leave them alone, they might wander over to have a look, but they’re usually pretty docile. If you don’t want them near you, clapping your hands or making yourself big with your arms and shouting usually makes them go away. I will say that you should absolutely not approach them if there are calves nearby and bulls in general are typically more aggressive, but if you keep a safe distance you should be fine

Cows, yes. Bulls, no.
Cows'll usually retreat from people. Or if they're curious, they'll approach but not too close.
Just don't walk behind them, or they might try to kick you.
Bulls are territorial. Stay the fuck away from 'em.
- Just don't walk behind them, or they might try to kick you.
  This is really good advice for basically every animal with hooves. They mostly have a blind spot directly behind, like horses:
  If you walk up behind them inside that blind spot and then move out to either side and suddenly appear in their vision, they'll react defensively, usually by trying to kick you with their hind legs.
  Basically if you can't see the animal's eyes then assume it can't see you, and stay out of kicking range.
  
  was kicked in the head like this once. Flew a meter into the wall
  
  What they say for horses is that if you're going to walk behind one, stay just behind it. That way if it does decide to kick you, the legs won't be able to build up momentum and will be mostly vertical before hitting you. Under no circumstance walk 1-2m behind it, you can die if it hits you in the head.
  Apply at your own risk to cows.

Extremely safe - just be careful about where your feet are if you're next to them. More people than you'd think have lost or seriously injured a foot because a cow or, especially, a draft horse, can't see where they're stepping.
If you get a chance and it's just cows then go up and say hi, they're wonderful animals and unbelievaby chill. I'd honestly be more comfortable petting a strange cow then a strange cat... if they shy away or noticeably get irritated when you approach be smart and give them space, but you're probably just going to get licked and mooed at.

Texan with a Ranch and cows here. They're VERY curious and goofy and stupid, and scared. Occasionally you'll have a lone bull in the herd try to intimidate, but they're scared too. The only thing to watch out for is look down where you walk so you don't step in poo!
- I grew up visiting my friend's family's cattle ranch all the time. The mean ones up there were cows, not bulls. There were a couple that you didn't want to get caught in the open with. I was chased up a tree a few times. Some cows just want to see the world burn.
  
  Lmao, interesting. I was just there this week and repaired something close to the fence. All of them, about ~50, came over to watch. I wonder if it's a breed thing? And you're sure they came at you to be mean, and not come see what you were doing?

Cows kills more people each year than sharks.
I mean when did you ever here of a cow killing a shark.

I never had a problem with walking around cows as a kid and I did it pretty often. Visitors would get spooked occasionally because cows love to follow you and see what you're up to, but I never got chased or anything. That was beef cattle country though so these cows were mainly cows (female) and steers (castrated males). I've heard that some bulls could be territorial however so your mileage may vary if one is around - the couple I've walked around were fine but your chances of issues are higher with them.

As the UK’s deadliest animal, cows attack between three and four thousand people every year.
An expert has revealed this figure may continue to rise. Between 2018 and 2022, more than 30 people were killed by cows, according to the UK Government’s Health and Safety Executive (HSE).
https://www.mirror.co.uk/news/uk-news/killer-cows-named-uks-most-30956262
- Deadliest other animal. There were 602 homicides in England and Wales in 2022/23.
- To be fair though, there are way more cows than crocodiles, snakes, sharks or deadly spiders in the UK.

Usually it's pretty safe except when there are calves on the field. It happens every year that some tourists (especially with dogs) go through a field with calves and their mothers and someone gets injured.

In addition to the other comments here: Don't run near cows. Quite often, they will start running with you, which is very impressive and dangerous at the same time. Cows generally are faster than you for the first few hundred meters at least.

a big factor here is dogs. if you have your pet with you on a lead, and there are calves(baby cows) in the field, sometimes a normally docile cow herd will be very protective of their offspring. generally if there is no dog, cows realise you are not a threat.

This reminded me of a time I went up and petted a cow and it turned and gave me the most wide-eyed horrified stare I've ever seen. I felt bad.

If there was a calf or bull around I wouldn’t walk through.
You can yell at them and they might disperse. If they don’t then you’d be able to walk through them.
Cows just don’t like to be startled, that’s about it.
- Where would you come across a bull though? I've never seen one in a field with cows.

We used to rent our farmland to the neighbors for their cows and horses. We would periodically have to go out there and do work on fences and the barn and stuff. I was always told that horses are not to be trusted, but the cows are probably fine.
Take that information and do with it as you will.

(also keep an eye out for where you’re stepping)

It really depends on what breed and how they were raised. In the Alps, there are almost anually reports of wanderers being attacked or even killed by cows. They often are with their calves for a longer time, are less accustomed to (strange) people and usually a fully intact male is in the heard that can get really protective.
Approach them with caution, watch their behaviour closely and use common sense. That’s what I do and for me that works.
- I had quite the opposite experience in the alps, we have hiked within meters cows because the heard was laying and standing on the path. I have never seen very young calves or bulls on the mountains.
  
  Well, then you were lucky. I‘ve been hiking off the beaten paths and more than once forced me an agitated bull to detour as he would not let me near his herd.

Adding to what the other comments have already said: Don't bring an unleashed dog on a cow pasture. You'd think that's common sense, but apparently it's a bit of a meme in Austria and Switzerland that every few months some German get's trampled by cows because their totally friendly dog ran towards the cows and they felt threatened.

Cows, sure. Just don't startle them or go near their calfs. They're mostly just curious.
Bulls, only if you have to, but make it quick and stay as far away from them as you can. They're fiercely territorial and not afraid to show it.

Stampede is the most common cause of death for backpack tourists in Australia. It may tempting to jump fences for a little shortcut, but many cows do not tolerate home invaders.

They're mostly safe. Don't taunt them, don't get too close to them (specially not to veals and bulls), and eventually they'll see you as "safe to ignore".

If I have to give only a binary yes/no answer, the answer is no. In reality, there are lots of variables ranging from breed, pen size, herd makeup, season, socialization, hunger, weather, and even more that would factor in. That's without considering the other variable of you as a person they don't know.
Edit: that's not even to say the cattle or a bovine would intentionally hurt you. They're big, sometimes clumsy, have horns, etc. I follow some youtubers who have been raising cattle anywhere from a couple years to most of their lives and they still are very careful in a lot of their movements and interactions.

NEVER STARE DIRECT INTO THEIR EYES

Id be a bit careless to say they are a hundred percent harmless but over all they are really shy and cerous creatures id probably say you were being just as shy and careful about them as they were being towards you so yeah they have the strength and weight to crush you and rip you apart but they at most accidentally use that capability bulls on the other hand as far as I'm informed are kinda like 100 ton dogs

Generally? Yes. Cows are animals. They will react to situations. Especially to you appearing between them and their children. Bulls can be aggressive, but that doesn't mean that they always are.

There's probably a lot of different variables, cows vs bulls, the breed, how they're being raised, if they have calves with them, how you're behaving, etc.
In general though, safest bet is always going to be to give them space and not approach them. Not to say they're necessarily going to be aggressive or anything, but that's just kind of rule number 1 with any animals you're not familiar with.
Annecdotally, when I was a teenager, I did Philmont, which is a big property the Boy Scouts of America (now changing their name to Scouting America) owns in New Mexico, where scouts can go backpacking. They also maintain a working cattle ranch there, and I believe so e of the neighboring ranches allow their cattle to (grave? Free range? Roam? I'm not sure of the correct terminology) the Philmont property, so it's not uncommon to encounter cows in various places there.
They give pretty much the same lecture, don't approach them, don't do anything to spook them, and give them some space.
At one point my group was hiking along a trail coming to a junction, and a few dozen cows came down the trail we were about to head up and went into the woods. We weren't super close to them, but it was probably about the closest I've been to a cow outside of a petting zoo in my life, and there was nothing but a few yards of open trail between us. We just stood back and watched them go about their business, the cows didn't pay any attention to us, we hung out for a couple minutes after they passed in case there were any stragglers, and sure enough there was a lone cow that came running down the trail trying to catch up with its friends.
I'm no cow-ologist, but my general understanding is that they tend to be fairly laid back, and if anything curious. That said, they're big, powerful animals and you don't want to spook them.

Apparently they are the UK's deadliest animal
https://www.mirror.co.uk/news/uk-news/killer-cows-named-uks-most-30956262#:~:text=As%20the%20UK's%20deadliest%20animal,and%20Safety%20Executive%20(HSE).
- That’s why we take no chances and mow them down with blue light vehicles.
  Police car repeatedly rams escaped calf
  
  Wow. Just wow.

Cows are usually very curious and nice. You have to remember that they are wild animals though and unpredictable. They could kill you by sitting on you.
If you act natural, don't make any sudden movements, than you're good. Also get out of the way, because they will just run over you. Especially in spring, when they get out of the barn for the first time since fall. They're blinded by the light and a little spring crazy.
Bulls are a different matter. You they're less sweet.

Don't know anything about this from personal experience, but I thought I heard a report a while back about a fairly large number of hikers in the UK injured or killed by cows. So I'm guessing, not as dangerous as crocodiles but still best to be careful.

Not really, man. Cows are like people, some of them are just assholes. Cows kill hundreds of people every year. If you don't know a cow's temperament, don't put yourself where it can kill you.

https://youtu.be/bnI_Y8PyTHM is an interesting perspective on cowology.