I have associated Classical music with riding, ever since my first teacher used to play records during classes to help illustrate and teach rhythm.
What I've found is that horses also enjoy music, particularly classical European music, but really anything that has a good, lively melody; music without too heavy a beat, with a pleasant melody, and with a consistent tone, i.e. no changes between very quiet parts and very loud parts, works well, no matter what genre. Very quiet music doesn't work in a large arena.
I haven't tried much music from other cultures, so I cannot say if other music works, but I'd bet heavily it does, since I've also played jazz and big-band and even dance-club which have antecedents in African music.
Of late, I've been playing a lot of Strauss waltzes, which gives a great rhythm for our exercises, both on the ground and in the saddle; as well it provides a feeling of warmth on these bitterly cold winter days.
With the music playing in the background, I seem to be much more co-ordinated and and don't unconsciously tense up, or get stiff, or find myself being being too demanding. I naturally move and work with a light feel and touch, almost as if I'm dancing, instead of riding.
Just something to consider.