Last of the Saddle Tramps: One Woman's Seven Thousand Mile Equestrian Odyssey (Equestrian Travel Classics): Messanie Wilkins: 9781590480434: Amazon.com: Books
This woman did it in the 50's. In her 60's when she did it.
Mustang Journal: 3000 Miles Across America By Horse: Lisa F. Wood: 9781882897865: Amazon.com: Books
This trip was done in 2000's.
The second trip, they actually drove it first to see where water was, where the safe places where and the terrain.
Both books would help you greatly.
The main thing is you would need to make sure you know what you are getting into, and have support system of some type set up too.
Some people are fine with a stranger camping on their land for instance. Other places you might get shot. This is a very big country, and the land varies from so hot you can bake and so cold you will freeze and so dry you will parch of thirst.
You also need to realize that in the winter months? There are places up north where you would not be able to do anything at all, period. You can die very easily.
I think this is doable but you would have to first find a horse here, and that might be harder than you think, or easier too.
Write or e-mail every single state you can for information on them, and also check for any people you know online who are horsey and in America.
I don't see why, with some planning and forethought, it can't be done.
Do you know where you want to start at?