You can look up Horse Hotels and Horse Motels on the internet, there are many. When I plan a long trip, I look for them and plan my day's travel accordingly. My personal max amount of time that I want to be in a truck is around 8-10 hrs, including all the stops, so around 400-450 miles/day. If I route my trip that way, I can look at a map and find towns/cities close to that distance on my route and then start looking for accomodations. Some will also have accomodations for people, but not always. When I've not been able to find a horse hotel along my route, then the horse or horses can spend the night in the trailer, you just need to make sure to feed them down on the floor and unhook their heads so they can drop them down. I try to only overnight in a trailer if I'm hauling 1 horse, that way he has the whole 3 horse trailer to move around in. I try to make sure they have at least 8-10 hrs not moving every day.
Also take a look at the weather and timing around metro areas on the days you plan on hauling. It can get dangerously hot inside a non moving horse trailer. Think about rush hour and construction traffic jams.