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?
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 an automatic weapon (I don't recommend) or outfitting yourself in medieval armour. (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.)
If you're in an area that has trees, however, a rope and grappling hook could get you out of the reach of wild horses - if you're quick!
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.