I put ice in gallon size zip lock bag (I get the ice at the vending machine at the resort) and place it in a soft side cooler backpack we got from Target and also place my Frogg Togg towel in the cooler. The ice will last all day. If we feel hot we find an air conditioned place and sit with the ice pack on face and neck along with the frog togg towel. So helpful. Just got back today and this worked great just like it has in the past. To prevent leaks I put the ice in a ziplock and seal it then place that ziplock bag inside of another 1 gallon ziplock. The bags can be reused the next day.
We did something similar on our trip end of August last year in AK - the hottest of any of the parks. We were both starting to feel ill from the heat so after EE we went into the bathroom and wet down our cooling towels for the first time on the trip and sat on the floor of the EE gift shop for 20 minutes. We weren't the only ones in there either!
After feeling well enough we made are way to the not so fast pass line at Kali rapids. We had rain ponchos but opted to just pray for a soaking which we got. Then we walked over to Nemo to watch the show. I've never been so happy to be freezing cold. It brought our core body temp back down to something more normal and we felt tons better.
So my take on staying cool if you can mix in outdoor rides with a water ride and air conditioned meals or attractions.
But don't be shy if you are getting hot sit in a gift shop or at a table in Dinosaurus in AK or Rays Starlight in MK noone will care.
Cooling towels are great when you really aren't able to cool down- as are the mister fans. I would say be careful with the smaller fans. I gave one to DD12 last year and in an instant she'd gotten her long hair tangled in the blades. Ugh
We brought a Brita water bottle and asked at the QS restaurants and snack stands for a cup of ice water to pour into the bottle in order to keep hydrated throughout the day -but sometimes i would just dump the ice water over our heads rather than into the bottle. They would not fill up the bottle directly
We wore dri fit clothing so continued wetness was never an issue
Also I would highly recommend Body Glide to combat blisters. We would rub the stick -that looked like deodorant -every morning on our feet and in between our toes and it worked like a charm. I've heard Body Glide is also good for areas where you may chafe.
And even though we like to go go go our strategy last year -as well as this year -is midday pool breaks. You'd be surprised how refreshed and energized you feel for an evening in the park after some time in the pool and a shower.