We've spent many years hanging around the stables in Sea Pines, especially my horse minded dd. Lawton Stables takes you on a nature ride through the Forest Preserve at Sea Pines which includes 5 lakes (you don't pass by all of them on the trail ride though), an ancient Indian shell ring; the guides are informative about the area and its history. The horses are matched to the rider's ability; most (if not all) of the ride is done at a walk; western saddles are used. Minimum age to ride is 8, unless the child rides at home (but if your child is 7 almost 8, I would call and ask--they might make an exception). The phone number 843-671-2586; Betsy and Tom the owners are really nice. Can't remember the exact cost to ride, either $40. or $45. for a 1 hour ride, but add on another 30-45 minutes beforehand to get the riders fitted to the horses. A reservation is needed, and during the busy weeks they can completely book up. Finally, bring some carrots---it's fun to feed the horses as well!
For younger children, there are also pony rides available for $5.
HTH!