Within the Sea Pines Forest Preserve [1] is Lawton Stables (190 Greenwood Dr., 843/671-2586, www.lawtonstableshhi.com [2]), which features pony rides, a small animal farm, and guided horseback rides through the Preserve. You don’t need any riding experience, but you do need reservations.
Links:
[1] http://www.moon.com/destinations/south-carolina/beaufort-and-the-lowcountry/hilton-head-island/sights/sea-pines-forest-preserve
[2] http://www.lawtonstableshhi.com