"The horse was sold to you fair and square"
Unfortunately it doesn't work that way. Sales of a horse are like a series of links in a chain. If one link is broken(one sale is illegal), all the links after that are broken too.
So for example a barn worker steals Mary's horse. He sells it to Joe. Joe sells it to Bill. Bill sells it to me. I have the horse. If Mary finds out I have the horse and approaches the authorities and has proof it's her horse, and the authorities contact me and inform me, I have to give the horse back to Mary. I bought the horse fair and square, but I have to give it back to Mary.
A couple scenarios possible.
1.) Two's did not finish paying One and took off with the horse to another state. One finds them, contacts the authorities, they contact me, I have to give the horse back to One. I bought horse 'fair and square', but the sale from One was not legal. That Two's gave the horse away is immaterial. The horse goes back to One.
2.) Two B disputes Two A giving the horse away. Two B disputes that A had the legal right to do so as Two B was not consulted in the sale. Two B's name is not on the bill of sale to Three (even giveaways need a bill of sale and something must change hands from buyer to seller - one dollar is fine). There is a bill of sale from One that names BOTH Two's as the buyer. The movement of horse to Three is not legal. I have horse. Two B contacts authorities, but A and B cannot resolve who should take the horse and they are no longer in business together. Typically, one owner will buy out the other's part of the ownership and the horse will go to that person. The movement of the horse from Two to Three is invalid and so is the movement of the horse from Three to Me.
3.) Two and Three are too preoccupied with their own current emergencies and crises and don't actually have anywhere to board or keep a horse. Plus, since Two's and Three both have things going on they'd rather not have attention drawn to, they very quietly lose interest in the horse. One sees a chance to make a pile of cash with very little risk, so throw a scare into Celtic Hill that they have some legal control of the horse. Celtic of course will do anything to keep the horse...and One has a lengthy and complicated explanation for why Celtic buying the horse's registration papers would make One forget all about how much he is dearly attached to this horse and misses it so.