Horses seem to be habitual animals. Whenever Hurricane Rita came through, that was supposed to be a Cat. 5, there was a mandatory evacuation. We sat on the road for 24 hours to go a distance that would normally only take us one hour. We had our mare and gelding pony with us along with all our other animals. Mind you, it was 100+ degrees outside with crazy humidity and no wind. It was torture. My mare didn't drink once on that trip. She was pretty badly dehydrated(I can't remember much as that was almost 8 years ago and I was just a child then.) Some people living in the area had the biggest hearts and took us into their home when we were planning on sleeping on the side of the road. Their neighbors had a pasture and stalls and horses, so our's got to stay over there. Luckily, my mare drank there. And how long did it take us to get home? Forty five minutes. It was ridiculous.
Anyways, you can lead a horse to water but you can't make it drink. Whenever I take my colt to a groundwork clinic, I'll offer him water 5-6 times in a couple hour time period and he won't drink the water right off even though he's drank the water before. Some horses are just like that. Does your horse have hay to eat while you're travelling? My colt will finish his dinner(that I soak well so it already has water in it), go eat some hay then go off to drink. Before I started soaking his feed, he would ALWAYS go drink right after he ate. He'd make a beeline immediately after finishing his supper. Do you know what times your horse normally drinks? Maybe you could try stopping at those times and offering him water then.
There on the tips of fair fresh flowers feedeth he; How joyous his neigh,
there in the midst of sacred pollen hidden, all hidden he; how joyous his neigh