When I travel with my horses I have found the best place to stay is fair grounds. You usually have an entire fairground to yourself if you don't the fairground the same time as the fair:D

I have also found this site to be useful: http://www.horseandmuletrails.com/ for researching places to stay.

I have stayed at fairgrounds before. Some are better than others. Some that I have been at you have to use buckets to get water into the stalls. It can be a lot of work.

you can also use horsetrip.com to find places to stay.