I got this around 4-5 hours into the game by essentially role playing. I did the things that I think I would do if I owned a horse: before riding I would pat him multiple times, every morning I would feed him, I tried to hitch the horse when possible. Also there were points where the story would have me hop on a different horse. When I could, I would whistle for my horse and swap out (for example the very first bounty mission). This is very easy to get as long as you take care of your horse.