If you're basing a horse pack in North America, a Western pack would be better than a Southern pack. When people talk about an American-based horses back, I think they're talking cowboys and rodeos. They didn't have either in the American south. (As far as Kentucky Derby, isn't that heavily based on English-style horsing culture? A British pack might be better for that, so the game could add some other elements.)
BTW, Western horse culture is not a Southwest thing. It includes southern and northern states equally. One of the most famous jobs of cowboys was to go on cattle drives that brought cattle from ranches in SW states to railyards in NW states. The cowboy culture was in all the states they passed through, partied in, and eventually spent their lives in.
I live in Minnesota, far up north. Most people who were raised up here know how to ride horses, knows somebody who owns them, and many went to horse camps as kids. You see a lot of people wearing cowboy boots, western shirts, and even cowboy hats. (The cowboy hats aren't as popular as they used to be though.) Everybody wears jeans. We have a lot of bars and restaurants with wild-west themes. Western art and wildlife art are both very popular. Country music is very popular (too popular imo). We have rodeos and country-western music festivals. It's the same way in Wyoming, Montana, and the Dakotas.
If I was designing a horse pack, I would probably base it in a plains state like Nebraska or South Dakota. A desert type place would also be great, but we already have a nice desert location with Oasis.