I don't. :P
Our barn doesn't allow us to ride if the heat index is over 90, and the horses stay in with box fans blowing on most of them. I hose my girl off if I have time to go out, otherwise I stay in the A/C.
We prefer to turn the horses out at night when it's cooler & less likely for them to overheat. We keep the windows & doors open in the stalls to keep the air circulating, and a breeze going, if there is one. They have water buckets in their stalls & hay, and then they are turned out with more hay & big water tanks.
I think it works pretty well, as our turnout does not have much shade- only two of the four pastures have trees/run in shelters, and so it's best if they are in out of the sun.
A couple of years ago (I don't recall exactly when) we tried putting a portable/mobile run-in shelter, like a mini-barn almost, in the fields without shade, but the horses refused to go near it, even if we bribed them with treats, hay, etc. They were convinced it was going to eat them. So again, we decided it was easiest/best if they are in during the day and out at night.
Alright, that was long enough.
I guess, as far as riding goes, it's best to only ride for say a half hour (not very long), have a goal in mind, and quit while you are ahead. Make sure to warm up and cool down extra carefully, and don't do hard work (jumping, gaming, lots of canterwork, etc). Afterwards, I usually hose her off and put her away, making sure she's got plenty of clean water.
My biggest pet peeve in warm/hot weather is putting a horse in a stall or on turnout without checking their water and making sure there is enough for them to drink, and that it isn't warm, dirty or otherwise unsanitary. My horse is a little picky with her water- if there's lots of hay or grain that's been dropped in her bucket, she's less likely to drink it. So you want to make sure your horse will drink what's there.
That was much more than my two cents, but I had a lot to say about it for once!