The park cannot store milk for you, but you can get ice from a restaurant. Frozen water bottles last a long time and work well to keep milk cold.
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Mini-refrigerators typically maintain temperatures under 40 degrees which is ideal for safe storage of things like milk, cheese, and yogurt. They usually also have a small freezer section and are deeper so can fit more inside.
Hydro Flask 21 oz Standard MouthThis is the only water bottle I use daily and it's the only one that I ever bring to the parks anymore. This insulated bottle keeps drinks cold up to 24 hours and hot up to 12 hours. Plus, it fits perfect in cup holders which is a massive bonus.
I recommend bringing a small cooler with ice packs to store your milk, since there are no public refrigerators inside the parks. You can store your cooler inside a climate-controlled locker rental for easy access throughout the day.
As you already know, visiting a Disney theme park in the summer means walking around in the heat for hours at a time. We highly recommend bringing your Cool Links® towel with you everywhere in the park, so you're never wishing you had it.
Guests are free to bring outside food and beverages into the theme parks as long as they do not bring any glass containers and they do not bring any alcohol, which means you are welcome to bring metal water bottles with you into the theme parks.
Can I pack liquids in my checked bag? Yes, liquids in containers larger than 3.4 ounces must be packed in checked luggage. There is no limit to the amount of non-alcoholic liquid that can be brought, but too many full-size bottles can exceed the maximum weight limit for your luggage.
It might be a good idea to bring a cooler with you, as temperatures can rocket in the summer months. If you don't have a cooler, a waterproof bag with ice packs will also help to keep your food cool.
If you choose to bring a cooler into the Walt Disney World theme parks or water parks, it can't be larger than 24 long x 15 wide x 18 high (61 cm x 38 cm x 46 cm). Keep in mind that loose ice or dry ice in the cooler is not permitted, but you can have reusable ice packs in your cooler or frozen water bottles.