These are some pictures of MesoAmerican pottery depicting men riding on deer and similar beasts. The bottow two depict dogs as participating in some way in transportation. The controversy surrounding the BoM claim of ‘horses’ could be influenced by these finds.

One LDS archaeologist, Mark Wright, summarizes his views on this subject (he provided the pictures as well):

Just for the record, I don’t think the ancient Maya rode deer as a regular form of transport, and I don’t think that’s what the Book of Mormon is talking about when it talks about horses. What I did want to show was that the concept of riding deer was not unknown to them, and demonstrated that with the images of the Moon Goddess riding a deer. What I do find fascinating about the images is the fact that the deer appears to have a form of a saddle, as well as some type of rein, which seems a pretty interesting detail for a people that never actually tried it – how would they know that some type of saddle/rein would even be useful? That and that fact that the word for “deer” and the word for “horse” is the same in many Mayan languages. It’s not my favorite explanation, but I find it plausible.

I actually prefer the dog explanation, as dogs are almost always found in association with the royal palanquin/litter/”chariot”, and horses in the Book of Mormon are always in association with chariots but never ridden. But I’m not entirely sold on that one either.

And then there are the mysterious horse bones sitting in drawers and bodega shelves that nobody get around to carbon dating because they just shouldn’t have been in the dirt in the first place. But I’ve never seen a drawing of a horse in the ancient record, so I’m not convinced of this one either.

The point is, although I’m not entirely sold on any of the explanations yet, I find all of them to be plausible and each has some support from either linguistic or iconographic or osteological data and therefore I’m not at all bothered by the “horse question” – I know that one of these plausible explanations is right, and I honestly don’t care which one it is.