Regardless of your plans, things can change. A breakdown, traffic tie-up, or weather delay can leave you far from your planned destination when you need to stop driving for the day. Before you hit the road, use the online directories of stables offering overnight accommodation and download the list of every stable along your entire route. That way, if things change, you have a starting point for finding an overnight stop.
Some of these are quite comprehensive; others have only a few listings. Some are updated regularly. Others may well have listings that are no longer accurate. Compare all of them and coordinate your route accordingly.
www.horsemotel.com (Includes stables throughout each state)
www.horsemotel.net (Focuses more on stables near interstates.)
Facebook has several groups that can provide leads for stabling:
FB group: Traveling? Overnights for Horses and their People
FB group: Road Apple Gang (Full Timers and our horses\mules)
FB group: HTCAA|Horse Trails & Camping Across America
FB group: Camping with your Horses\Mules
Boondocking is the term for camping far off the track in wilderness or totally primitive conditions. Often that will be in state or national parks or designated wilderness areas.
FB group: Boondocking with horses
If you need a veterinarian while on the road, the American Association of Equine Practitioners maintains a directory of veterinarians by location: https://aaep.org/horse-owners/get-dvm