Never deny a horse water. Ever. When I compete in CTRs, we must keep our horses moving forwards once we pass a certain point. No stopping to eat, rest, circle, backtrack... But we are allowed to walk our horses slowly past a source of water and see if they will stop on their own accord and drink. "Always let them drink" is a set in stone rule. Water is very important on the trail. If a horse wants to drink, by all means let them drink. :)
I would say the odds of dehydration are higher than the odds of having a little cold water tummy trouble. I've seen more dehydrated horses on the trail then I've cared to, but never a horse coliced on water.