Some considerations:
How will you support yourself in the new location? Are you independently wealthy or will you need a job? Will your work qualifications get you employment where you are looking? If this can be accommodated then you are OK to start looking at other things.
Is there a large area of public land where you can ride? Remember that the land must be open to horses (be it public or private).
How long is the “commute” from house to trail head? In some place you’ll measure in minutes and some in hours.
Are you campers or do you consider “roughing” it the HI Express instead of the Crown Plaza? That can make a difference.
Do you want just “wilderness” or are more prepared venues (like National Military Parks or National Parks or State Parks) more to your liking?
Are you hot weather people, cold weather people, or do you care one way or the other? Do you mind riding in the rain? Snow?
We live in East TN, about midway between the Great Smokey Mts. National Park and adjacent National Forests and the Big South Fork National River and Recreation Area. Pull up Google Maps to see the extent of these public lands (one of the largest groupings east of the Mississippi). There are also several private riding venues in this area (particularly around the Big South Fork). There are also several Military Parks (Chickamauga, Shiloh, Stones River, etc.) that have trails. Many State parks in TN and GA have equestrian trails. I’m less familiar with KY or the Carolinas. Weather is temperate with warm, but not overly oppressive summers, really nice falls, really wet springs, and only very modest snowfall and cold. You’ll lose a few days in summer due to heat and a few in winter due to cold. Rainfall is abundant, meaning lots of green trees and high humidity! Cost of horse ownership is generally reasonable. As you move west across the state you find less riding opportunities as you approach the Big Muddy and Memphis. It’s generally a good place to ride.
There are other good areas along the Appalachians but colder as you go north and hotter as you go south.
The western mountains are the next most logical place to look but are somewhat more demanding in terms of weather. From my recent visits to CO and from people who live there it’s filling up with people from further west. The biggest advantage is LOTS of public lands but also growing restrictions at the State and Federal levels. I personally like New Mexico as another place of reasonable climate and opportunities to ride.
Google Maps will be your friend in this process as you will be able to see the big and detailed picture of any given area.
Good luck in your search.
G.