Hey if the OP wishes to register her horse then why not? The grade horse registry might be one solution. It is at least proof of identification if the horse should be lost or stolen and on a broader scale it would help keep track of lineages (not that I am suggesting a breeding program, don't get your knickers in a knot people).
Here is the website: American Grade Horse Registry (AGHR)
I don't honestly know how legit the registry is but it may be worth looking in to.
Additionally, if you ever wished to sell the horse on, it may be an attribute in the eyes of a potential buyer, regardless of if the papers serve an actual purpose or not.
Oh and I think AB used to rule Munchkin country and once had a close run in with a falling house from Kansas