i did see water fountains in the parks but never seen anything with cups for ice water. we general brought a water bottle with us and just kept on filling it up as we went
I think that Disney will give you cups of water at any cs location. I can't see them denying anyone water in that kind of heat. Would almost be a liability.
FL water tastes TERRIBLE though. T-E-R-R-I-B-L-E. DS was 20mos when we were last there and he outright refused it, and he was always a water drinker. He'd give it back and say "Not Water! Want WATER!!"