I have a friend who was a travel nurse (pediatric) for many years. She loved it and has lived in and explored areas all across the US (although I don’t think she ever went to Alaska).
She did not have a horse, but given what I know of her lifestyle during that time, I can’t imagine being able to keep a horse with you. Many of her assignments were in large urban areas where boarding stables were both distant and very expensive. Plus, she often worked like a dog, long hours and minimal time off, because they were short-handed (hence the need for travel nurses).
Technically, she had a choice of where she went, so theoretically, I guess, you could select assignments in areas where it would be feasible to keep a horse. However, in reality, when one job ended, she had to take another, and she had to pick from what was available at the time - sort of a least worst choice situation - so there is no guarantee that you could pick horse-owner-friendly locations.