I work at the racetrack (steeplechase) every Spring and Fall, so that is what I'm basing this off of.
After the races, the horses are untacked (right on the field) and walked back to the stalls. If the temperatures are high, they are hosed off right on the track (it's all grass) before walking to the stall area. They're handwalked for about 30-45 minutes -they're HEAVING - every few minutes (less than that really, there's buckets of water every 10 feet) the handler deliberately stops and offers the horse water. If the horse motions towards the water bucket, they're allowed to drink. Mind you, they're still heaving from the race. They're hosed off at least once during this handwalking session, sometimes more than once if the temps are high.
I don't even know how many horses I've seen at the track. 6-12 horses per race, 7 races per day. 42-84 horses per day. I've never seen one tie up from being cold hosed while still heaving from a race. I've never seen one have any issues taking in water.
As for eating, I won't let a horse eat until he's cooled down, but I don't know if that's superstition or not.