I was watching a show called "Big History" and they pointed out that a pivotal point in human history was when man domesticated horses (and camels) for riding, allowing much greater mobility. They indicated that Native Americans were at a loss in this area, which contributed to the lack of civilization development due to lack of cultural interchange (aggravated by the N-S orientation of Mt. ranges compared to E-W in Eurasia.
It seems to me that the ungulate in N America which is parallel to the horse/camel is the American Elk. Yet I've never heard of one being properly domesticated, much less broken to ride.
Imagine riding into battle on one of those things!