Yes, those spray bottle/fan things are great at the parks. We got ours at Target and were like portable air conditioners. You don't need one for each kid, but they are cheap so it might be a good idea to get one for each so there's less of a chance of fighting over them.
Disney also has begun setting up small covered areas in the parks where they spray you down with a cool mist, so use those whenever you can. I clearly remember there being one in Tomorrowland and another in Future World in Epcot not far from Test Track. If you're not sure where they may be, ask a cast member. Use play fountains whenever you see them (Toontown and Epcot).
Wear a light-colored hat with a brim that goes all the way around the hat to keep the sun off your face, ears and neck. I've seen them in the parks with lovely logos and characters on them (kid-size too), they make great souvenirs. Better that the really silly hats you'll never ever wear anywhere but WDW. (When will you wear the cap shaped like Mickey's glove?) I have dark hair so my head gets really hot, and my hat was a lifesaver. You can just roll it up and stick it in your bag or waistband on a rougher ride.