As soon as we get to Orlando we stop at a supermarket and buy a couple of cases of bottled water, then take it to the hotel and put them in the refrigerator; some to be frozen and other just cold. Then when we head to park we take a bag with at least 1 bottle of frozen and 1 bottle of just cold water for everyone in the group. If we have rent a locker we do, but usually I just schlep around with the bag that gets lighter as the day wears on. We might get some soft drinks when we eat in the park, but water works much better at hydrating you than sodas that usually have caffeine that actually causes you to urinate more and lose more water.
We try to avoid the local water they give you at service counters because it tastes horrible. I honestly wonder if Disney add bad flavors to the water to try and convince people to buy bottled water or cokes.
No, it's the standard Orlando tap water taste....