I don't think so. There is no evidence across the Americas of the Incas, Mayans or any of those cultures having any sort of beast of burden.
Well, the Incas used llamas for hauling stuff. Also, the landscape was different in Central and South America. While that's also home to the jaguar, it would stand to reason that the cougar in North America would pose a similar threat to wild horses (which wouldn't be that much, apart from the old and infirm, the sick, and the very young).
I'm not aware that there are any surviving images of the horse in the Central American writing systems. But then, I wasn't trying to make that case.
The Message of the Engraved Stones of Ica by Javier Cabrera Darquea
http://members.cox.net/icastones/exerpt_index.htm
I understand these artifacts are considered to be a hoax - but as there are more than 10,000 Ica stones, I'm keeping an open mind.