We usually take our horses with us when we can. Most parks & places we go don't rent horses. This is not a Dude Ranch but you can camp and rent horses.
https://www.rattlesnakesaloon.net/ in Alabama.
We did drive the motor home to Bryce Canyon and rent horses. I highly recommend Ruby's Campground (I believe they rent horses) but we used
http://www.mechamoutfitters.com/
None of these are Dude Ranch Experiences but great places to ride. Also whoever said horses are expensive, very true. Much cheaper to trail ride and camp than show. When fussing about the price always remember. Good horses aren't cheap and cheap horses aren't good. Takes a good horse for some of these trails.
I will be following this thread, and we will take our own horses. Thank you.