It's been a long time since I've done the horseback riding over there, but if I remember correctly, they have both an age and a weight restriction. You have to be over x amount of years to ride and weigh less than x amount of pounds. Unfortunately, I don't remember either what age/weight the restriction was set to. We used to go to the campground all the time, and I personally don't remember doing the horse riding until I was at least 7 so I'd probably take a wild guess and say they probably won't let a 2-3 year old on a horse. I could be wrong though. And its been at least 15 years since I rode over there. I'll do some research and see if I can find anything.
Upcoming Trips to WDW:
Dec 6-10: Disney Wonder
Dec 10-19: Port Orleans French Quarter