I would not stop every 3 hours. Offer water when fueling, or using rest rooms.
I also would not trailer at night and rest during the day, as that is much hotter on horse, and more tiring too. I'd do driving from 7 to 5 ish, give or take, and find your overnight spot. Time it so you will arrive at your destination in the daytime hours, which may mean you stay overnight 2 nights.
That way horse can settle in and be able to see what is happening.
Add Gatorade to your horse's water now, powdered, so that when you offer it on trip, might drink it better.
Be alert when you stop, and always after leaving your trailer, check your hookups, hitch, and all your doors to make sure no one has done anything to your trailer.
Make sure you have a trailer aid so that you can change tire if you need to.
And secure everything in bed of truck as the wind will whip around in the bed and carry out every single thing you have in there, even things you think it won't.
Find the spots you will be overnighting in, and find out if you need your own hay/buckets or what have you, and if they have a place to drop trailer if you want to.
And don't get your horses out to "let them walk around", that is dangerous and a good way to get one lost too. I've seen people walking their horses around letting them graze at rest areas which is just flat out foolish. We've all seen our horse refuse to load easily, plus, most rest areas spray their grass for weeds.
And too much danger for you yourself if you are trying to load horse and someone comes along that is dangerous. Be alert to your surroundings.
Horses make me a better person.