I think that a were horse would have to come out of an entirely different tradition than currently recognized weres. What would be the gain, what the danger? A horse does more than run, but what if you the kind of were you are is determined by what happens to you when you first change?

Say, in a culture that lives close to the earth, at adolescence the magic rises, so they go out to a spirit journey. Somebody gets scared spitless, has to run like mad, and ends up turning into a horse. Why a horse and not a deer, elk, horned antelope, etc.? Have to be somewhere where horses are known? Can you only become a creature you're familiar with?

Or are there meddling gods/spirits that choose the horse form simply because there aren't horses around?

There is a fairy tale tradition of a horse that has to be kept on an iron bit to keep it from changing back into a person, and some associated story that involves selling someone a horse that gets free and runs off.

It's an interesting idea you have here. :)