Do you have the original papers for it, or any paperwork, was it ever registered, and do you have a transfer, and know the registered name?
You need to call the association and ask them what you have to do to register the horse, and what it will cost and tell them what papers you have, or don't have and let them help figure it out.
If horse has changed hands some, without benefit of papers that went with it, you might have to track all of them down who were prior owners too, and that can be more trouble than it is worth.
Was the horse a rescue that you have gotten from the rescue, or?
Many rescues will not let the papers go with horses of course.
Horses make me a better person.