I'm NOT the dancer that Dancing Arabian is, but I did take ballet, tap and acrobatics as a youngster, then went back for ballet and tap post HS. DH pulled me into 3 years of ballroom dancing, too, but health concerns (his) put that on hold. Our instructor, also owner of the place, was a Chinese acrobat, now US citizen, so he understands physical workouts. I trusted him, and the teachers he trained.
The point is that any structured dancing is a way to teach you balance. If you think that you have 2 left feet, you really have a problem balancing your weight. You can learn to do so. Unless you are young--under 25 imho--ballet would be difficult bc those dancers stretch and hyperflex before, during and after class. An older, stiff person could really strain muscles and do harm to their backs. So is hip-hop. Tap is more forgiving. Ballroom dancing can be learned at any age. We had a guy in his 80's in our classes doing very well.
DA, I still have my book on belly dancing, and I've dabbled in it over the years. THAT really loosens up your spine. I HIGHLY recommend that riders learn to dance, especially ballroom dancing bc as you learn to follow your partner's cues you gain a better understanding as to what your horse goes through trying to figure out how to follow YOUR cues.
You also benefit bc you become more limber as you ride. When you ride a horse you contract your thigh muscles. It becomes more difficult to stretch your thighs, but it makes them stronger when you do both. Happy dancing, all!! =D