DS (aka The Milk Monster) prefers his milk at close to room temp, but he won't touch Parmalat. He absolutely hates the way it tastes. (To be honest, I don't like it either; IMO it has a rather metallic taste.) You might try her on it ahead of time. If it's a bomb, here are some tips for keeping regular milk:
As I said, I live with the Milk Monster, and we travel a lot, including overseas, so I'm an old hand at keeping milk in hotels. If you are doing the whole baby-in-stroller thing at WDW, it isn't that hard to keep regular milk cold in your room, or even in the parks. Even if you don't have a car, if you do a grocery stop you can buy a jug and a reclosable pint bottle, along with a small styrofoam cooler. (Or you can bring a small collapsible cooler in your luggage.) The hotels have tons of ice available.
Here's the trick for the parks. Fill the pint bottle (or even 2 of them if your kid just can't live without milk) about 3/4 full, then put it in a paper bag with your name on it, and take it to the food court. Ask that it be put in the freezer for you; they will do it (I've never had a US hotel refuse to put something in the freezer for me.) Pick it up in the morning as you head out and keep it in a bottle bag inside your diaper bag; it will slowly thaw over the course of the day. Putting a ziploc of ice in with it prolongs the effect.
BTW, some children will prefer water in the parks when it's hot. In fact, too much milk may lie heavy on the stomach and make them ill in the heat. DS only drinks milk or water, but the only time he will want milk at FL parks is when we go inside for lunch. If we're outside he is better with water.
(BTW, I'm not kidding about DS being the milk monster; he's 6 yo, and he has a 4-gallon a week milk habit. We don't carry it in the parks anymore, as we usually go to a hotel for lunch as we park-hop, but we still keep plenty in our room.)