Just because you don't know how their contract works when a horse is returned, doesn't mean they haven't handled that well many times.
how does a person recoup anything when a private sale goes wrong?
Here's what happens. You call them back. You say the horse is not working out. You want to bring it back and you want a refund. Oh, and if they'd pay you for the vet exam too, that would be nice.
Then guess what happens? The seller says, 'too bad', and hangs up, and that's the end of that. You have a horse you don't want and maybe can't sell, and you have no legal recourse. You can't afford to get a lawyer, and the sale was too much to go to small claims court. You dump the horse at a kill auction, and get a few dollars? Or maybe give it to a friend.
The private seller says he already got another horse, and has no free stalls, can't take the horse, besides, you had your chance, why didn't you figure out whether you liked the horse or not before you bought it. Etc, etc etc.
Private sellers very, very rarely will take a horse back, especially a cheap one.
Occasionally, well heeled, well known dealers will let you exchange one horse for another - another that's in their barn at the time, and costs either less or the same as the one you got.