If I'm training or just simply riding, theres really not a chance to stop for a drink. They are cooled off before I get off them though so by the time they are kicked out to pasture or put back in their stall, they are ok for water whether the myth is true or not. I let them drink on trail rides though, and if I'm in the arena with the huge water barrel, I stop to offer a sip.
I used to work as a polo groom though and many people would hose down SWELTERING HOT horses that were still heaving for breath and dripping sweat, fresh off the polo field. I always heard this was a good way to tie a horse up, but out of all the horses I saw in multiple polo matches and practices, none of them did. Is it also a myth to wait to hose the horse off until its cool? Again, I never saw any of them react badly to it. The first time I saw it I almost fell over, but I'm guessing I've seen at least 200 horses who were hosed off while still HOT with no bad reaction.
I'm too chicken to do it to my horse for fear of a bad reaction.
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.