My guess is this happens it's a RDO horse and it's not supposed to be ridden in Story, though I honestly don't know why it won't show up in the stables. So I saved my game, reloaded and now my gypsy had changed into a tennesee walker.
It's like the game doesn't recognize I'm actually riding a second horse. My original horse was still following me because I can't stable that one either. It still wouldn't show up, so I couldn't do anything like change tack or give it a name, but when I exited I was still riding it. Second time I tried I first put my saddle on the gypsy and then rode into the stables. I rode in on the gypsy (no saddle) but when I exited I was back on my first horse and the gypsy had disappeared completely. The first time I tried the gypsy wouldn't show up when I rode into the stables and it wouldn't let me stable my original horse either.
I can saddle it and bond with it just fine, but the game won't let me stable it. So I used the Lenny trainer to spawn in a splashed piebald gypsy cob in early chapter 2, right after the mission with the bear.
