I'm in Florida and it gets unbearably humid, long sleeves, even moisture activated/ wicking ones are too hot here.
I like a pair of thin tights in a pale color and a tank top made from 100% cotton with large arm holes and if possible mesh sides for more ventilation.
If it's particularly warm I kind of like to do something that's considered a 'no-no' and ride in shorts, but only bareback. I made the mistake of trying it in a saddle and ouch is all I have to say on that one.
But as everybody else has said try to ride early morning or later at night and carry water. Also along with the cooling towels (which do work ten times better than a wet bandana.) I'd suggest taking a bottle of alcohol or witch hazel and mix it with water. If you get too hot (or your horse) you can wipe it on and it has a cooling effect, just keep it away from your eyes of course. Then rinse it off and reapply if needed.
"They see me rollin, They hatin, Patrolling they tryin to catch me ridin dirty"