Have you talked with your doctor? I'd probably start there (and, if you were going to ride with a therapeutic riding facility, you'd need a doc's assessment).
I think the biggest issue is just managing fatigue. You'd want to be sure you're working with a quiet horse with really steady movement (some horses just require more energy to ride if they have "big" movement), and be sure you were communicating with your instructor about when you needed a rest break or to change up the activities. You'll also want to talk about how much of the grooming/tacking up you want to take on prior to the riding portion of your lesson, as those prep activities can require a surprising amount of energy.
Every person is obviously different, but generally, therapeutic riding can certainly be beneficial for people with fibromyalgia.
Good luck! Glad you've enjoyed your horse adventures so much up to now.