You might be interested in this paper by Yvette Running Horse Collin, a doctor in indigenous studies: https://scholarworks.alaska.edu/handle/11122/7592

Chosen excerpt:

Although historians generally claim that the Indians of the Southeast first acquired horses in the 1690s from the Spanish, there is written Spanish record of the Southeastern Indians having been seen with horses as early as 1521 in what is now Georgia and the Carolinas. This is particularly interesting as it would have been impossible for the first horses that the Spanish brought to the mainland (what is now Mexico) in 1519 to have escaped unnoticed, “make it” to the Georgia and Carolinas area, and have multiplied in two years’ time.