It's hard to tell what might be best without knowing more of the context - how much "conversation" is going to be directed to the horse. In a lot of situations it simply wouldn't be necessary to include it at all, but it's also possible to envisage a scene in which the horse(s) are more directly involved in how the scene unfolds.
I don't have any problem with "hup, hup" in dialogue - although I don't know how you might express some of the other non-verbals. The first time you might explain whatever commands you decide to use, but after that I think it should be fine.
I haven't been on a horse since I was a kid, so about the only thing I'd be saying if I found myself on one now would be, "Get me down from here," or maybe just, "Help!"
