Historical information: Nephi would have done us all a great favor if he had left his comment to "there were beasts in the forests of every kind. . ." and "all manner of wild animals...". However, he had to vex us with the problematic "cow and the ox, and the ass and the horse." None of these animals has a clear attestation in the New World, and particularly in the Limited Tehuantepec area.
There is no clear cut explanation of these terms in the Book of Mormon. In the case of the horse, there are possibilities of modern horse bones found in pre-Contact levels of some sites, but these are controversial and have not yet been thoroughly discredited nor vindicated.
For the other animals in the Book of Mormon for which there are no clear counterparts, the suggestions range from a common linguistic convention typical upon encountering new species (an argument favored by Sorenson, see 1985 pp. 288-299) to substitutions on the part of Joseph Smith during translation. There is no clear cut argument that can carry the day. There is also no reason to deride the Book of Mormon for such minor inaccuracies. As Sorenson points out, the early Spanish Father Diego de Landa called the small brocket deer a "kind of little wild goat." It is certainly possible that we are seeing here the naming problems common when an established language must describe animals for which there are no terms in their native tongue.