When I did endurance and CTR, We always encouraged our horses to Drink at every opportunity they came across. And we let them drink as much as they wanted.
Most P&R rest stops we put lots of hay and some grain in front of them. We usually feed Alfalfa at the rest stops because it packs more calories per lb than grass hay and contained more calcium which horses use to trigger muscle twitch.
Unlike a performance horse that must preform for a 6 second calf roping, a 16 second barrel run or a 2 minute cutting drill. Distance horses need to perform for 5-6-8 hours. Performance horses can compete in their short events using the energy stored in their muscles. Distance horses MUST refuel on the go. Meaning they need to be processing food in their gut all day. They can not store 8 hours of energy. They need to eat and drink consistently thru out the event.
I dare say that distance horse that will finish a 50 mile endruacne race in 5 hours or even the slower horses at 8 hours, will be hot and sweaty. As long as they are working, Let them drink what they want.