We just did the horseback ride this past weekend.
It is $46 per person. You can go to the kennel at Ft. Wilderness. There is an outside window and ask about availability over the next couple of days. We asked on Saturday, and were able to book a ride for Sunday right then. There are 3 rides per day. You report back to that same window 30 minutes before your ride time and pay for the ride then and sign a waiver form. Maximum weight is 250 lbs for the rider. There is a minimum height and age (I'm thinking 48" and age 9). The horses are already saddled and waiting for you when you arrive and you are given some simple instructions as you mount. You ride single file through some trails around the Fort at a walk.