Are there any online horse roleplaying games where you can actually see yourself as a horse and move around

Furcadia. It's not strictly a horse roleplaying game, but there are plenty of sections within it to roleplay horses, like Pryor Mountain, Hollowood Reserve, etc. On top of that, there are some really cool people there.

Virtual Horse II and Virtual Horse I. Or VH1/VH2, I can't remember what they called it exactly. Anyway, if you google it, you'll find a download.

That's all I can think of right now...feel free to make improvements, anyone.