Not a 'dude ranch' but there is an RV park near Custer SD that has stables and livery horses. We have stayed there and found the sites a little to close. It did have FHU and you could bring your own horses. View of the Cathedral Spires there in the Hills was great. I have no idea of the trails or properties available to ride.
Is is Broken Arrow Campground and is off local rd 793 south of hiway 16 on the east side of Custer City.
I should add, I checked this morning and found they have expanded the size of the CG as well sites. Now it has cabins and 'mess hall' and meeting hall.