When my husband's uncle was 87 years old, he dropped by to see us while I was riding the TWH that I had back then. He said that he loved gaited horses and wanted to ride. We pushed, pulled, and got him up on the horse. He didn't just walk around. He put her into a nice quick rack and then he cantered around the yard a little bit. After about 15 minutes of what was obviously a great time, he came over and asked me to help him get down. He said, "If I fall off and break something, everybody is going to say, 'That old fool should have known better.'" He lived to be 100.
I think that being willing to do fun stuff kept him going. I am glad you got your dad to ride.
Painted Horse - check into a therapeutic equestrian association in your area, they are n't just for kids. They provide side walkers and there are portable oxygen tanks he can carry over his shoulder like a purse. Might do him some good!