It's not clear to me why this post is on the DVC board, but here is the riding info. I have an AP and as far as I know there are not discounts on riding but I am not positive. There are also hay rides and pony rides at FW by the way, but since you only asked about horses here you go:
Walt Disney World guests both those staying at a Walt Disney World Resort and those visiting for the day are invited to enjoy a 45-minute guided trail ride through the natural beauty of Fort Wilderness Campgrounds & Resort. This trail ride is a walking paced ride, which is fine for beginners. Up to twenty riders per adventure will join two Walt Disney World cast members several times a day on this relaxing and enjoyable ride.
Guests are asked to arrive thirty minutes prior to departure during which they are introduced to their horses given a few rules of the trail before setting out. Departure is from Fort Wilderness Trailblaze Corral at Tri-Circle D Livery. This is located at Fort Wilderness Campground guests services.
All trail ride descriptions and price information subject to change. Call Walt Disney World directly to confirm details.
Reservation are required and can be made up to two weeks in advance For reservation or more information call (407) 824-2832
Some Things To Know Before You Go
Rides offered daily at 8:30 am, 10 am, 11:30 am, 1:00 pm, 2:30 pm, and 4:00 pm
Ride times may vary seasonally
Cancellation of rides may occur due to inclement weather.
Cost is $32.00 (plus tax) per rider
Rides must be 9 years of age or older
Maximum weight of 250 pounds (113kg) per rider
No double riders permitted
Suggestions for comfort and safety include
Hats not recommended except for baseball style caps
Cameras and pocketbooks not recommended to be carried during the ride
Shoes must be worn with open toe or high heels not recommended
Long trousers are recommended