Horseback riding?

I'm applying to the JET Program, and one thing I'm trying to take into consideration for my placement requests (although I know those are far from guaranteed) is where I would best be able to ride horses, and more importantly, if the horses in those areas are actually well cared for. I've read a lot about horses in Japan receiving very poor care, which is something I know I wouldn't be able to stomach.

The prefectures I currently have on my list are Oita, Kagoshima, and Miyazaki. Am I likely to find quality stables in those areas? Is there somewhere else I should look? Or am I better off if I just forget about riding for whatever amount of time I spend in Japan?

I can't speak for the places on your list, but Gunma has a number of stables. A friend of mine has seen riders in nearby Saitama as well and has mentioned them to me. I've never been to any stables here, but a (different) friend went to one in Gunma (one in Maebashi I think) and enjoyed it a lot, said they were really good. She didn't mention anything about care though. I've also seen pamphlets around for Gunma stables, but they all look like they're English style and I ride Western, so I've never bothered to do more than look.

I'd just do a general search to find some stables, then realize that even if you request those places you may get put somewhere completely different that may or may not have any stables at all, so just be flexible.