Mainstream scholarly thought is that American Horses died out about 10,000 years ago and remained extinct until they were reintroduced by Spanish conquistadors.
In a presentation called Science and the Book of Mormon, given at the eleventh annual FAIR Conference, 6 August 2009, Wade E. Miller mentions carbon-dating done on horse bones found in America. Many of them date back before the known extinction date for horses in America, but a few have dates ranging from 1400 to only 800 years ago.
In the final paragraph, he says,
"Horses weren't here in America after about 10,000 years ago according to Smithsonian archaeologists. As you know horses ... are mentioned as being present among both the Jaredites and Nephites. It might surprise most of you that the history of the horse is mainly here in America. The very first horses come from North America, and their record goes back to about 58 million years ago. Horses were small, forest dwelling animals at the time. It wasn't until much later that horses reached the Old World, being roughly the size of modern forms then. Columbus only reintroduced the horse to America. I've actually done a lot of work with fossil horses from many areas and from different periods of time. A lot of my work has been done on them in Mesoamerica, primarily in Mexico. While the vast majority of dates for these various kinds of horses are well before man was known in the New World, a few of the dates are very surprisingly young. I have Carbon-14 dates on horses that are as recent as 800 years. Other dates are only 1200 years to 1400 years ago. More dates in this range are needed to be able to convince others that horses were indeed here before 1493, when they were reintroduced. Other paleontologists have produced dates on fossil horses that show they lived here long after the 10,000 years before stated. This slide is of a partial horse skeleton that was put together with my colleagues in Mexico. An earlier slide showed the location where it was collected. It was that picture that I said to remember from Durango, Mexico, where a lot of fossils were found within one small area."I look forward to reading about the details of these and any other results he may have found.