Interesting. I think the AIHR has it right because these horses are all basically the same breed. They're very closely related.
Maybe you should do more research since the plain Indians disagree with this article and claim to have had horses long before the Spanish came....
I believe that because you can detect some ambiguity in the statements about breeds. I believe that the Native American horses were present. Some ones political agenda is probably why theyre trying to convince us that European were the source of horses only.