Well, my folks just bought a piece of land out in BFE Colorado, next to a woman with a grandfathered piece of land consisting of 21,000 acres right off the Pawnee grasslands. She can easily volunteer her acreage to the government if she so chooses. She raises a herd of cattle, has a few horses. Each horse is a down-home Quarter Horse with plenty of miles put on them, though. So, I do partly disagree with Jamesqf in regards to the nature preserve thing. Only partly.
If you're looking for something "exotic" to have on a farm, you need a feasible back-story as to why such a breed is in such an out-of-place location. Cattle farmers like their stock horses. They don't have time for or want hot-headed messes running around. You might consider having this horse belong to a daughter - as was suggested - who was big into the English style of riding and show jumping or dressage. If that's the case, you're looking into Warmbloods, Thoroughbreds, Lippizaners, Lusitanos, or you could get into the drafty breeds and look at Gypsy Vanners or Friesians. All of these are "exotic" and would be highly valuable with the right paper history and bloodlines. You might also consider looking into QH/Paint bloodlines, finding the best of the best, and having your horse be an "exotic", or at least an eye-catching color. Cremellos, Perlinos, Duns and Palominos, Champagnes, Silver-dapple black/bay would all be eye-catching, pretty to look at, and out of place when found on an abandoned farm. http://www.lacyquarterhorses.com/qua...e-sales-36.JPG
- Dun http://www.angelfire.com/oh5/bluemoo...adeToOrder.jpg
- Palomino http://www.horsecoursesonline.com/co...s/image014.jpg
- Perlino http://4.bp.blogspot.com/_mJ4Kw54b5q...0/DSCN3087.JPG
- Silver Dapple http://arabians.jerland.com/horses/crystal_blue-01.jpg
Remember that beauty is in the eye of the beholder - if this "young girl" has always dreamed of horses and is a horse advocate, even a simple old 20-something schoolmaster type horse will be beautiful in her eyes. In the end, color/breed/etc is up to you as you're the writer.
As far as surviving, yes. With that much acreage I don't see any reason why a horse wouldn't be able to survive, especially with open access to water and food. You might consider looking into wildlife in the area you desire, as I've seen pronghorn, elk, and deer all keep horses company in many areas throughout Colorado. In a sense, it's no different than a horse buddying up to a goat - only, pronghorn are just like really big goats. This could make it feasible for your horse to survive alone. You might want to get realistic and have this horse covered in scabs and such, as mosquitos and other bugs would be sure to bite him up, burs wouldn't magically be removed from his main and tail, and he'd be sure to get bumps and bruises over the course of a few years.
I agree with the others - the level of his regression would largely depend on how he was handled before. This needs to coincide with your "exotic" horse's back history. If you chose to do just a wildly colored QH, it could be that the horse was green and hardly handled before humans left, leaving plenty of room for him to develop into himself over the course of the last few years. If you go with the original owners having a fancy horse for their daughter (or something like it) I do believe he'd be skittish but his training would make itself known, as someone else mentioned above. Or he'd have had to have been seriously abused. So really consider what you've gotta do to make it feasible.
On a side note, if you're going to have a small girl get her heart set on this horse, please be practical and try to avoid advocating the impractical approach that is shown in so many stories. Try to avoid midnight treks to a round pen, where she slips in between the fence panels and tries touching the horse. Please.