I've never ridden with my ipod, although I would love to try it. My main concern is that I wouldn't be able to hear my surroundings, so I would probably only ride with one earbud in. I do think it could be beneficial to ride with the rhythm, in theory, at least, it could probably get a person to relax and loosen up.
At the last barn I boarded at, they had a boombox that I was going to use but it only played like two radio stations and that cd player was broken in it. My current barn has a sound system in the arena but I don't have control over it and it's usually turned down pretty low anyway. So, ipod is pretty much my only option. I might have to try it next time I ride! :)