You can reserve the Fort Wilderness trail rides ahead of time. So if you know for sure that you want to do it, go ahead and make the reservation. It's in the middle of the afternoon, so just be aware if you're going at a warm time of year.
Ft Wilderness also has wagon rides 2x every evening. It leaves from outside of Pioneer Hall. Cash only. $12/adult and it's a bit less than that for children. No reservations, first come, first served. Fort Wilderness and the Port Orleans resorts, I believe, also do carriage rides which I think you can book ahead of time. It's on the WDW website.