Sounds like you've got a little cowboy on your hands, Andrea. My two youngest kiddos did pony rides at Tri-Circle-D Ranch at Fort Wilderness a couple of years ago. They had a cute little meandering path on a dirt trail within a fenced area. My husband led my daughter's horse and I led my son's. It was a very low-key experience, yet my kids still remember it as one of their favorites!
As for your reservation times, the pony rides are only available until 5 o'clock. If I were you, I'd plan to arrive around 4:00. The pony ride will easily be accomplished in thirty minutes. You might want to leave a bit of time to explore the playground and beach at Fort Wilderness (all within walking distance from
Tri-Circle-D). If it were me, I'd probably schedule my dining reservation for around 5:00. Be aware that the area outside of the restaurant will be thick with guests of the
Hoop Dee Doo dinner show at that time, but it shouldn't impact you. The safe bet is to plan for an hour for dinner. After your meal, you simply walk outside to where the carriage rides load (it's visible from the "porch" of Pioneer Hall). It's literally a minute or two from the restaurant. Just in case dinner runs long, I'd schedule the carriage ride for 6:30.
Sounds like a perfectly festive day. Enjoy the trip!