In one of the guidebooks I have there is a place called "Horse World" in Kissimmee. Their website is www.horseworldstables.com. I have never been, but it was the only one I saw advertised.
If you've ridden a horse before, then WDW horseback riding will be pretty tame for you. It's great for beginners in that it's a 45 min. WALKING trail ride. The horses are very tame and walk nose-to-tail with a CM leading and bringing up the rear. If you are beyond that (could be boring), I'd check out Horse World.
if you like to ride, the place to go is the Grand Cypress Equestrian Center...
it's at the Hyatt Grand Cypress (actually near the Villas of Grand Cypress)..
they have an English stables on one side of the property and a western trail riding center on the other side of the property..
i haven't been to the western trail center, but the English stables are one of the finest in the entire United States.....a truly outstanding equestrian center and highly recommended...
here's their website: