After all, when Cortez and his horses arrived, the Aztecs simply called the unfamiliar horses "deer."
See
http://en.fairmormon.org/Book_of_Mormon/Anachronisms/Animals/Horses/Loanshifting:_deer_and_tapirst
So the use of the word "horse" in the BOM instead of the word "deer" makes perfect sense!
/pretzel
It works for santa!