Critics who claim that references to "chariots" and wheeled conveyances in the Book of Mormon are anachronisms ignore important contradictory evidences.
It is not certain that the "chariots" had wheels. It might be assumed but it is strange that there are no references to wagons, carriages, or carts in the Book of Mormon even though they are all mentioned in the Bible and were very common in Joseph Smith's world.
Chariot use among the Book of Mormon peoples is mentioned only twice, both times in association with King Lamoni (Alma 18 and 20). No other king is mentioned have a personal chariot. If chariots were common this is unexpected.
The other reference is in conjunction with an effort to consolidate resources in preparation to battle the Lamanites:
And it came to pass in the seventeenth year, in the latter end of the year, the proclamation of Lachoneus had gone forth throughout all the face of the land, and they had taken their horses, and their chariots, and their cattle, and all their flocks, and their herds, and their grain, and all their substance, and did march forth by thousands and by tens of thousands, until they had all gone forth to the place which had been appointed that they should gather themselves together, to defend themselves against their enemies (3 Nephi 3:22; emphasis added).
The context was for the chariots to assist in bringing in the “grain and all their substance.” Neither horses nor chariots are mentioned in the ensuing battle (3 Nephi 4:7–14).
The precise animal and conveyance reference in the Book of Mormon are not known. The original writer (Alma) and the compiler (Mormon) would not have possessed any firsthand knowledge of Old Testament chariots. Joseph’s understanding would have been limited to Biblical descriptions.
Wheels would have been made from wood, which would not have endured over the centuries. Clearly, the wheel was not widely used, if it was used at all.
The use of chariots as described in the Book of Mormon is different from their uses as described in the Bible. They are never mentioned in any of the wars or battles in the Book of Mormon. However, they are commonly highlighted in Biblical accounts (see Exodus 14:25; Judges 4:15). David had “a thousand chariots” (2 Samuel 8:4; see also Exodus 14:7). The chariots of Egypt, Babylon, and the Philistines are feared super-weapons upon the plains of Israel.
Excavated toys demonstrate that the wheel was known. This is from about 450 A.D. discovered in Mesoamerica.
Researchers acknowledge that 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. Current excavations are very limited compared to the areas that could be explored in order to more fully understand the early peoples of the Americas, including their modes of transportation.
FAIR Issues 42: Dismissing Book of Mormon Geography Inaccuracies, Michael R. Ash, 0:07:22
FAIR Issues 55: Do Nephite Names find a “Home” in Middle East, Michael R. Ash, 0:07:54
Faith and Reason 11: Book of Mormon Politics Unlike Joseph Smith’s, Michael R. Ash, 0:08:52
Faith and Reason 19: Deseret and Bees, Michael R. Ash, 0:05:09
Faith and Reason 20: “Without a Cause”, Michael R. Ash, 0:04:35
Mormon FAIR-Cast 109: Response to criticisms of the Book of Mormon, Martin Tanner, 0:19:50