I believe there is calling the park would be your best choice it's been a while since I've been there
There is a place to camp and ride your own horses. Prude Ranch rents horses and does trail rides. There is water at the camp site but not much else. All horse trails are across the road from the main park. No horses are allowed in the main park, but the equine area is very large.
You can get them outside the park. Plenty of beautiful ranches around there to go riding on.
Check w the park, I believe there may be across the road in a primitive area. There are some dude ranches in the area. Prude ranch is one that offers horseback riding.
I don't think in the park but there might be some programs that offer it outside the park.
We just got back from there. Not aware of any horse trails or horse facilities there.
Thanks! Your answer is awaiting moderation.