Get on a horse, man!
The first thing I’ll need to do is stock up on supplies for myself and my horse before I can begin my journey. It’ll take roughly a day to do all of that. The first significant challenge will be crossing the Rio Grande, which isn’t all that scary except for the snakes. On my way over the Texas badlands, I’ll encounter a decent number of steer rustlers. But because I’ll be alone, they won’t trouble me at all.
After there, it’s on to colder climes in Montana, where I’ll only stop to resupply and avoid being chased by gunslingers on my horse’s hooves. It’s just going to take a few months.