For years LDS apologists have tried to find the remains or other evidence of pre-Columbian horses. One such attempt is the statement by Daniel Peterson in this video. 

He refers to horse bones found in the upper Mid-west that says preliminary reports identified as being contemporaneous with the Book of Mormon accounts.

Apparently Peterson was referring to — and was taken in by — one of the most persistent archaeological hoaxes of recent years.  You can read about it here  No responsible archaeologist believes that horses existed in the Americas in the time period of the Book of Mormon.

Up until recently when they took down the post, BYU’s official Maxwell Institute site pointed to a horse found in Florida carbon-dated to 100 BC.   However,  in private correspondence I asked Dr. Bruce J. MacFadden, the University of Florida’s Florida Museum of Natural History’s Curator of Vertebrate Paleontology:   “What is the latest, pre-Columbian date for which we have carbon-dated proof of the existence of horses in the Americas?  Does your research lead you to believe that horses were common in the three thousand years before Columbus?”  He responded:  “About 10,000 years ago. There is no evidence of horses the 3,000 years before Columbus. –Bruce MacFadden”  (email to the author, dated 3-17-08.)  When told that he had been quoted in support of pre-Columbian horses in Florida, MacFadden responded, “That is not an idea that I support.” (email to the author, dated 3-17-08.)

Unicorns, Pegasus, Centaurs, and Book of Mormon horses. All fictions.

Read more about the horse controversy in  The Mormon Mirage 3rd Edition:  A Former Member Looks at the Mormon Church Today (Zondervan, 2009)