as long as you don't bring a grill, whole roasted turkey + the fixins, or a can of corn, alcoholic drinks, or emu legs... you can bring water bottles, and other food items.
I belive that glass bottles are prohibited, but any plastic water bottle you want to bring in is fine. Lots of people take bottles of Deer Park or Dasani in with them to avoid paying the extortionist prices inside the parks, and lots of others carry sports bottles that they refill at drinking fountains.
Gotta love Disney! I would suggest bringing a plastic refillable bottle, with plenty of ice when its hot out!
DM and I wound up buying the little bottles of water b/c by the time we finished those they were already warm Probably cost more money in the long run, but it kept us cooler!
Brita makes (or used to make?) individual water bottles, with filters on the top. You fill it up and as you squeeze the water through the sport-bottle type top, it goes through a small charcoal filter. We always take those & never had a problem.