Oh yeah, I forgot about that - Parmalat. There may be other brands. You have to kind of look for the juice box sized bottles, and it isn't inexpensive. It also coms in maybe quart sized boxes. It might be worth bringing some Parmalat from home.
Not to belittle the point, but if you are only getting a fridge to keep milk cold to drink for breakfast, you are probably just better off getting your milk in the food court/gift shop when needed.
When we tried the cooler, we needed ice at least twice a day. We used a softsided cooler and ice in ziplocs. Leaked every time we tried it.
I'm not trying to criticize others, just sharing my experience. We've tried just about every method, and found that if you are only talking milk and orange juice the savings really isn't that great.
Another factor to consider is that the savings on groceries is only there when we actually eat all the food we buy. The only exception, IMO, is bottled water. Staying hydrated will save more than just the cost of the water.
I also like to look at the overall cost of the vacation. Time is money. A trip to the grocery store during your vacation equals time you are not out having fun. If you subtract what you are paying per hour to be in Orlando from how long a shopping trip costs, the savings is even less. You are probably better off paying Disney prices for food. I say this as someone who has looked at actual receipts and how much we 'saved.'
DDP is one of the best deals for our family.