My experience from two trips to Punta Cana is that the only horseback riding you can find is from fincas that do not care about the horses at all. The horses are emaciated to the point that one wonders if they will live beyond the week. On both trips I asked the kitchen chef staff for zorahorio crude (sp?) - raw carrots - to bring for the caballos. In both experiences it took the animals a good ten minutes to realize that what I was offering them was food. After which, they were overjoyed and eager to follow me for treats.
I will reinforce my comments by saying that I believe in keeping pets lean, for their long term health. This went far, far beyond. I would truly love to find a place in the DR where I could take healthy, well fed horses for a run along the beach. If I could, I would bring a few sacks of good quality oats for the horses along with the school supplies I bring for local children.