In some parts of the western United States there are herds of wild horses. How dangerous could a herd be to a human on foot while hiking or backpacking?
If they are dangerous how should a human protect themselves?
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Obviously, since horses are animals, they are relatively predictable (they have known behaviour patterns), but can be very unpredictable (they are autonomous creatures).
Note first that horses are not predators. In other words, they're not out there to get you. The only case in which they become a threat to humans is when they feel that you are a threat to them. Even at that, in general, they are somewhat like deer; if they feel threatened, their first instinct is to evade the danger.
However, they are tougher animals then deer, and they are well aware that they can defend themselves to some extent: their legs are so powerful they could kill you. (Reference)
So the answer to your first question is, yes, horses can be dangerous to humans if they feel threatened.
In answer to your second question, the major aspect of protection is prevention. Keep a safe distance between you and any wild horses you come across - this article suggests 50 feet as a good minimum distance. Obviously, the more horses there are, the less threatened they will tend to feel, therefore keep a greater distance.
There's not a lot you can do as far as protective gear is concerned, short of carrying a weapon (I don't recommend). Pepper spray or other chemical solutions won't do a lot of good since they're coming at you. You might get the horse, but he might run you over in his terror.
Play it safe. Don't get too close to wild horses (no close-ups with a 50 prime), don't make loud noises: avoid frightening them in any way. And, oh, by the way, if you have a good telephoto and are taking pictures, be sure to keep one eye out of the viewfinder from time to time.
I have had multiple encounters with wild horses in an environment where they are used to the presence of hikers. There was an obvious pattern where approaching within a certain distance (which isn't the same for each horse) would cause the horse to switch from natural behavior to wary behavior. Any approach beyond that point would result in rapidly increasing alarm on the horses' part and the person doing it would be promptly warned by others to stay back.
However, if one was standing still the horses would approach well within this distance without showing any worry and I have had an incident where a horse wished to go somewhere that due to terrain and a rail forced it to pass only a couple of feet from me. It was obviously wary but nothing like it would have been had I walked that close to it.
I have had a similar experience with some other such animals that I was told were bighorn sheep (but I'm not at all sure of this!) where in their grazing they approached to about 20 feet from me with only a few glances at me (and I wasn't completely still--I had my camera out, taking pictures.) When I moved away a couple of other people moved to the same spot--and now the animals looked quite worried, enough so that I would have gotten out of there promptly. (Again, this was an area where hunting was not permitted.)