It's been soooo hot everywhere lately, and I cannot imagine not having a fan on the horses!!
I assume she is worried about the fire risk. When we were barn shopping, some facilities provided fans, others did not.
We are super paranoid horse owners so we wouldn't board anywhere without a fan. Where we are at now is a private farm, no other boarders, just the barn owners chickens. They, the BOs, did not want a fan hanging from our two horses stalls due to the aisle being full of extension cords, one of which got wet and electrified the metal siding on the stable building. So, they compromised, knowing the horses needed a fan, but not wanting fans hanging from the stall front or having extension cords running through the aisle....they bought a huge 60 inch barn fan that we set in front of their two side by side stalls, and they get tons of air. they have dutch doors and they hang their heads out the door and their forelocks blow around so much it looks like they are doing a photo shoot!!! lol
Both ends of the stable have walls that are doors, and both huge door/walls are opened, as is a small side wall which is at the wash bay, so they have open walls on both ends and a small wall/door on the side.
I understand your barn owner's caution on this matter ....however, as a horse owner, I want my horses to stay cool in the brutal summer heat.....so I wouldn't accept the no fan policy. On the other hand if the barn was rigged with extension cords, I wouldn't be happy either....
So, it is a catch 22 situation.
I do think a good solution is to get a huge barn fan and blow it down the aisle for air circulation. I know our stable building can get very hot and stuffy, so just sticking your horse in the barn gets them out of the sun, but barns can get hot and stagnant.....a barn can heat up and become like an oven.