I would put them in our barn if it was done but we just put a bunch of dirst for the base or the arena/stalls and it is 10 to 15 degrees warmer in there if I had stalls and the arena finnished (im hoping soon) they will be going in there during the day.. and we will be putting a fan up on them outside today or tomorrow.
You can lead a horse to shade but you can't make them stand there.
My horse is out 24/7 but is in a huge paddock with lots of shady trees but she refuses to stand under them. She would rather stand by the gate in 100+degree weather and blaring sun. She was drenched in sweat yesterday when I went to see her.
Oh well, she is drinking and doesn't seem to be feeling unwell. Guess she isn't bothered by it.