Intriguing questions, and of course Doe has great responses. My take is, no matter what anyone thinks, you CAN'T think like a horse: to have almost no sense of time, but in nearly a perfect globe of space, and everything in motion-- what's it like to be in a school of fish? A flock of birds? We don't know. But we have to start somewhere, and if everything is anthropomorphic, what other way is there, reallY?
Our concept of leadership-dominance is as good a place to start as any, humans being somehwat obsessed with Who's The Boss. As I've gotten older, I like to start more like a "benevolent fence post", neither here nor there, but that's a little outside the topic, except that I think it's as natural as anything else.
Lucy Rees' "The Horse's Mind" is a pretty good fundamental book. Have you seen it?