There are a couple of horse "ranches" (sorry I don't know the correct term) west of Freeport on Hwy 20. I don't know what they do there, or if they are even businesses, but they obviously have large barns and pastures. It may be worth a shot...
Kelly Plantation, in Destin, has horse stables. I don't know how much they charge for boarding, and of course it isn't in SoWal but you may want to look into it.