Why don't we retitle this subject "Horse Won't Drink When I Want Him
To".....?
A horse ("brought along" correctly) will drink when they drink.
If it isn't at a time optimum to successfully do whatever is being asked of
it, then (after enough attempts) find another horse who can, who will.
If I was moving cattle for several days and my horse didn't drink or eat
(read, "take care of himself properly to do the job we need to do"), I guarantee
you I'd be riding another horse when next we moved cattle for several
days.