@ETpro – I base my information on the spread of European horses and cattle in the New World from a research project I undertook using observations recorded by Spanish and French priests in original expedition notes, beginning with Columbus’ time and going forward to the 19th century. Gotta love the Spanish – they wanted everything written down, and they kept all of it.
One of the priestly jobs was to inventory the New World, which they did very carefully on a day-by-day basis. You can track the spread of the European horse through the New World by their accounts, as well as the reception horses and cattle got from the American peoples.
Where the confusion seems to come in is how to differentiate fossil horse species from the European horse. There were many species of Equus in the New World, just not the precise species Equus ferus caballus. Equus ferus did evolve first in the New World, but there is a period of several thousand years up to the time of the Spanish arrival where there are no horse fossils to be found anywhere in the New World. And when the Spanish and French arrived, there were no horses in use anywhere.
About 15,000 years ago Equus ferus was a widespread, holarctic species, meaning it occurred throughout the Northern hemisphere. Horse bones from this time period, the late Pleistocene, are found in Europe, Eurasia, Beringia, and North America.
Yet by 7,000 years ago, the horse became extinct in North America and rare elsewhere. By the time of that extinction it is quite possible that humans in North America had either domesticated the horse, or treated the horses in North America as they had the horses from whence they migrated. As this one expert points out:
“Our findings show that the mammoth and the horse existed side by side with the first human immigrants in America for certainly 3,500 years and were therefore not wiped out by human beings or natural disasters within a few hundred years, as common theories otherwise argue.”
The reasons for this North American extinction and world-wide population decline are not known at this time. However, it was very clear when the Spaniards and the French first arrived that the native peoples caught on to the idea of the horse very quickly, and within 10 years were raiding ranches to take away horses and cattle both. Community memory as represented by oral history could definitely have preserved the memory of the horse in the Americas, making its reintroduction seem to be the meeting up of old friends.