The key to traveling with horses and keeping them from tiring from the trip is to shut you truck engine off at every fuel stop and make a fuel stop about every 2 hours. The lack of vibration from the truck lets them rest and recoup.
We do a good deal of traveling with horses. If we can not find a fairgrounds, a rodeo ground, a horse motel or whatever, we never hesitate to leave them in the trailer overnight. We will usually stop somewhere before dark and have our evening meal, and take the horses out of the trailer while we have our meal. The far back of big truck stops is a typical location, or we sometimes just stop at one of the on/off ramps of the interstates. And there are many smaller truck stops that don't usually mind if you unload in their back lot, so long as you ask first. It is not uncommon for use to spend 3 or 4 nights on the road, and have never had any problems with the horses.