I usually use 2 water bottles to get me through a day. I've got 1 big bottle (1/2 gallon) that I keep in the fridge in the breakroom, and drink out of that bottle during breaks, and use it to refill my smaller bottle. (note: this option doesn't really work without a breakroom fridge, but you could keep a larger water bottle in a backpack/diaper bag/small cooler) (note #2: I got my half-gallon water jug at Walgreens, but I'm sure there are other places that sell them)
The smaller bottle is a 20 oz bottle in a (slightly insulated) case with belt clip, that I wear on my belt. I usually completely fill this bottle, and freeze it over night. Then I take it out of the freezer, and wear it all day long. Even with the body heat, there's usually still some ice in the bottle for 4-5 hours, which works out well since most of my shifts are 6 hour shifts.
Most (all?) counter-service and sit down restaurants in WDW will give you a free cup of ice water if you ask. Outdoor merchandise stands (that only sell bottled drinks) won't be able to do this.