North America didn't originally have horses. When they were brought in, the Apache, more than any other indigenous group, structured their entire way of life around them. At least, that's what I learned from Western movies.
Now, I've read that horses were native to the Asian continent and migrated elsewhere, eventually to the Americas. However, I was at the San Diego Natural History museum last night and they had a display that claims the opposite, that horses are native to then migrated out of the Americas.
*37 seconds of Wikipedia browsing did teach me that native horses went extinct in North America about 8,000 years ago, then were later reintroduced.