I didn't have the problem until 13w21a, but I didn't ride too much. However, I've found that after breeding, the horse will move again. It has affected both my named horse and my unnamed donkey, although primarily my named horse, and it was never a problem before I named him with either of them.
Edit: After some experimentation, it seems that they're frozen whether you're riding them or not. They stand in the same place even when you're not mounted on them, and although they'll rotate and eat, they will not move. Giving them a single punch seems to work; after starting, they'll begin to move on their own, and then can be saddled and ridden. Don't call PETA.
Groovy Noob
I didn't have the problem until 13w21a, but I didn't ride too much. However, I've found that after breeding, the horse will move again. It has affected both my named horse and my unnamed donkey, although primarily my named horse, and it was never a problem before I named him with either of them.
Edit: After some experimentation, it seems that they're frozen whether you're riding them or not. They stand in the same place even when you're not mounted on them, and although they'll rotate and eat, they will not move. Giving them a single punch seems to work; after starting, they'll begin to move on their own, and then can be saddled and ridden. Don't call PETA.