Many of the beverage stands have the frozen slushies. They will cool you down in a flash. I couldn't manage the summer months at WDW without them! There is a good one right after you exit Test Track, it looks like a little car wash. I recommend the raspberry/lemonade, the blueberry has that fake chemical-ish taste. They have a large sized slushie there for $2.50, around WS they are about $4 but have many more flavors.
I also see people carrying the parasols from China. I'm sure it makes great portable shade, but I wouldn't want to have to tote it everywhere.
Then there's always good old cold water. We're supposed to drink 8 glasses a day, more in the heat. Dehydration and heat exhaustion are a big issue at WDW.
I have also seen the special bandanas that you soak in cold water and wrap around your neck. Haven't tried those yet. They sound good in theory.