Horseback riding is avalaible at the Fort Wilderness Campgrounds and is open to anyone who wishes to participate.
Here is the info from the CM web pages
Guided trail rides through a wooded portion of Disney's Fort Wilderness Resort & Campground; lasts approximately 45 minutes to 1 hour
Daily 8:30am, 10:00am, 11:30am, 1:00pm, and 2:30pm
All guests are required to check in 30 minutes prior to ride leave times.
Price:$30.19 + tax = $32.00 per person (total)
Reservations are recommendedand may be made by calling the Recreation Reservations Line at (407) 939-7529 or through any WDW Resort Guest Service location.
NOTES:
Minimum age is 9 years old
Minimum height is 48 inches
Maximum weight of 250 pounds, please
Helmets are recommended and are provided at no charge.
Nothing can be carried while on horseback. Small storage lockers to hold cameras and backpacks are provided at no charge.
Reservations may be made up to 90 days in advance
No open-toed shoes, flip-flops or strapless shoes should be worn for riding.
Guests must pick up tickets on the same day at the Fort Wilderness Resort & Campground Kennel at least 30 minutes prior to start of ride.
Please allow for extended transportation time from other Disney resorts
Parents need to sign consent form for children