Critics who claim that "horses" in the Book of Mormon are anachronisms ignore important contradictory evidences.
The words “horse” or “horses” are found fourteen times in the Book of Mormon. In light of the numerous passages speaking of group travel, migration, and war where horses might be naturally mentioned, this seems to be a surprisingly low number.
Critics who claim that “horses” in the Book of Mormon are anachronisms fail to explain why the role of horses in those societies is so different from their usage in Joseph Smith’s day. Horses and chariots are associated with travel, but the horses are never ridden. There is no mention of horses being used in agricultural activities. Also, horses are never used in battle or as a cavalry.
Multiple verses group horses with animals used for food suggesting that the horses, whatever species they were, may have been a food source.
Definitions of the word "horse" may have been expanded to include new meanings. The process of “translating” the plates was never explained so the word horse may have originated with Joseph or through a process involving the scribes. For example, LDS anthropologist John L. Sorenson suggested that one candidate for “horses” are "tapirs." A Mesoamerican type of tapir (tapiris bairdii) can grow to be over six feet long weighing more than 600 pounds. Some anthropologists and zoologists have noted the tapir's features to be similar to those of a horse or a donkey.
On three codex-style painted vases from the late-classic period of Mayan culture, ca. 700-850 A.D., there appears to be evidence that Mayans did in fact saddle and ride deer. These ancients used non-horse animals in ways that we today think of as "horse-like." This is not just speculation, real evidence exists showing this to be true. Click here
The late British anthropologist, M.F. Ashley Montague, a non-LDS scholar who taught at Harvard, suggested that the horse never became extinct in America. According to Montague, the size of post-Columbian horses provides evidence that the European horses bred with early American horses.
Some archaeological evidence for horses has been found. In 1957, at Mayapan in the Yucatan horse remains were found in the ground at a depth consistent with a pre-Columbian origin. Other similar remains have been found by non-LDS researchers. Multiple other excavation sites report horse remains including cave excavations in 1978 in the Mayan lowlands.
It is possible that horses were present but their remains have yet to be excavated in abundance. The Bible states that Abraham had camels while in Egypt, yet archaeologists long believed this to be an anachronism. Camels were thought to be absence from Egypt until the Greek and Roman eras. However, more recent research indicates that camels were used by the Egyptians from pre-historic times.
It is impossible to prove something did not exist. The process becomes more difficult if the translation of languages is involved because it may be impossible to accurately identify the thing reportedly absent.