I usually just read on this forum, but had to join to address this thread. Please, PLEASE contact an attorney before you do ANYTHING. Laws differ depending on the state, or even locality. Further, a lot of the advice you have been given has been incorrect and may end up costing you even more money. One thing I will say, GENERALLY you will not be able keep the horse AND get your money back. Obviously, if the horse is unable to be registered, there is SOME leeway to that general rule. However, it is HIGHLY unlikely that you are going to get to keep the horse, get $4000 back, plus all your costs. Or even the majority of that.
This is why I am stating that you need to speak with an attorney to actually determine what you ARE entitled to and don't waste a bunch of money suing for amounts you will not receive. (I honestly think this situation SHOULD be able to be resolved outside of court since the ONLY thing you are out is the registration papers. What happens now between the original owner and the seller is really of no concern to you as long as you get the registration papers.)