It's hard to tell if the old owner is just forgetful, lazy or malicious.
How about 'none of the above'?
As has already been stated numerous times, registration papers DO NOT denote ownership, and JC registration papers are basically useless
unless the new owner plans to race the horse or breed for the racetrack.
The horse was untrained and just taking up space. I hardly think there's some nefarious plot afoot for the previous owner to try and reclaim the animal at some later point in time.
OP, you should also be aware that a first right of refusal/give back clause is unenforceable, so even if you decided at a later date you don't want the mare, you're under no legal obligation to give her back to her previous owner. Moral obligation now, that's another story.