The horse riding is at Fort Wilderness Tri-Circle D Livery.
You call this number to make a reservation at least 2 week in advance:
[font=Verdana, Arial, Helvetica, sans-serif]00 1 407-824-2832
Cost is $32 each including tax.
Heres' some more info. I found on t'internet:
[/font]Guided horseback rides are offered 5 times daily (8:30, 10, 11:30 am, 1, 2:30pm) at the Tri-Circle D Livery at Fort Wilderness. The rides, which cost $32 per person, last approximately 45 minutes. Riders must be at least 9 years old and can weigh no more than 250 pounds. The horses are tame and walk pretty much single file during the ride. If you're an experienced rider, this ride may be too dull for you. If you've not had an opportunity to ride a horse before or have done so rarely, this ride may be just what you're looking for. To make reservations, call (407) 824-2832. It is strongly suggested that you wear long pants and that you do not wear open-toed or heeled shoes. To get to the Tri-Circle D Livery, you can drive to and park in the Fort Wilderness Visitor parking lot and walk; board a Fort Wilderness bus at the TTC and take it to the resort; take the Fort Wilderness boat from the marina at the Magic Kingdom to the Fort Wilderness marina and then walk to the Settlement Depot bus stop where you'd then board an internal bus to the Outpost Depot.