You may want to consider bringing a kitchen bag to use as a liner in the Styrofoam cooler.
Last September while staying at the Pop Century, we went to Wal-Mart on Turkey Lake Road to get a cooler. The Styrofoam coolers were $2 and change and were located in the main entrance of the store. That evening, we loaded the cooler up with ice and tasty beverages. Several hours later we awoke to the sound of water dripping on the floor. I was not expecting the cooler to leak. The following Day we went to Target, where I purchased a small box of large sized kitchen garbage bags(the white ones). I used a bag in the cooler as a liner. It kept all the water from escaping onto the floor. This year when I return, I will bring a couple of bags with me.