It's not just with horses, many animal rescues have that kind of clause in their contracts. I've volunteered for a few different animal rescues (dogs, cats, etc.) that required the adoptee to bring the animal back to the shelter in the event that they couldn't care for it anymore. Now, enforcing that rule is another matter. It's more of a feel good measure for the shelter than anything else. Most of them aren't in well enough financial shape to actually take someone to court over violating the contract, so it's kind of a moot point. You decide to sell the horse (or whatever) and they find out about it (and that's a big IF), they more than likely aren't going to do anything about it. It's the same thing with the clause that many of them include that says they can come to your house for a wellness check whenever they want to. It's nice, but do they really come out to check? More often than not the answer is no.