Here's another option to buying a Styrofoam cooler. Some people will buy a small cooler (similar to the size of the Styrofoam coolers at the supermarket) use it and then give it too another family to use asking only that they past it on when they are done, that way they don't have to try and lug it home and they can feel good about a friendly gesture. If that option doesn't seem to fit your plan another idea would be to buy a collapsible cooler. They will fit nicely into a suit case then expand to use during your trip. They are very nice and convenient to use again and again to take on picnics, camping etc...
I'm not trying to make anyone feel bad for buying Styrofoam coolers it's just that they are really bad for the environment. I realize they are cheap though and convenient (I have used them in the past) but I just thought I would mention a couple other options.
Disney does such a great job of teaching our children to protect the environment in so many ways (they even had a separate recycling bin in our room at CBR last year) that as visitors it would be nice if we could too

Like I said not trying to preach so please don't anyone feel like I am condemning those who still choose to use the Styrofoam coolers.
Just in case anyone is interested here are some facts about Styrofoam and other garbage.
http://www.smma.org.lc/news/jun99/plastics.htm
Time it takes for garbage to degrade:
Nylon Fabric 30-40 Years
Leather up to 50 years
Tin cans 50 years
Plastic 6-Pack Holders 100 Years
Aluminum Cans and tabs 500 Years
Glass Bottles 1,000 Years
Plastic Bottles and Styrofoam Indefinitely!