You can warm milk the same way you would formula; put the smaller cup (sippy or whatever) into a wider bowl of hot water; the fat refillable mugs work well for this.
Where are you staying? If you have a freezer, you can freeze the milk into milksicles using bottle liners, and carry them in a mini-cooler with a ziploc of ice and a cloth diaper on top to insulate it. They will gradually thaw, but stay cold enough not to spoil, at least up until about 4 pm if you insulate them well. If you don't have a freezer, you're buying at restaurants; it will be about $1.50/glass.
DS has always been a serious milk junkie; he goes through 2 gallons a week. At WDW, we keep a gallon in our room in an ice chest, and he has it for breakfast and at night. We will buy milk with his meals, but we have him drink water from a Brita bottle the rest of the time. (He doesn't like any other sort of drink; he only wants milk or water.) BTW, he didn't like his milk cold for a long time, but did eventually learn to prefer it that way, TG.