I sold a nice horse once. I fully explained what he was like, he never once bucked or anything like that, ect ect ect. Months later the buyer emailed me yelling at me that the horse is rearing ect with their trainer, that I lied, blah blah. I did NOT. I am NOT responsible for what happens in his life/training after he leaves. I have no idea what the "trainer" did to cause the bucking issues, but in the 7 years I owned him (since a yearling), never once did he do that. I was 100% honest with the buyer, but she did not believe me.
Horses are living, breathing beings, with a will of their own. Often times the DO change. Maybe the seller lied, maybe not. You agreed to pay $1000, you checked out the horse, IMO you DO need to pay the rest, UNLESS the seller is super nice and agrees to take less. I wouldn't if I were them. I MIGHT offer your $500 back and take the horse back. MAYBE. Not if I was honest about the horse's training ect and now the horse is bad, I'd wonder what you did to cause that (I am NOT saying this is the case or that you did anything, it's just what I would think if I were in the seller's shoes). I would offer to take back the horse with no refund.
Bill of sales are very important, clearly stating everything. They're important for both the buyer and the seller. Even when I BUY a horse, I bring one in case the seller doesn't have one. Two copies, one for me, one for them.