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.
