We were there at the end of June and there was a small freezer. I did exactly what you plan to do. What worked great for us was to have 2 sets of ice packs, one to go with us in the morning, then when we came back to nap and get ready for the night I would repack bottles, etc. and have nice cold fresh new nice packs ready to go. Worked great!! The fridge was good size also. We had 2 (1/2 gallons) of milk in it, a bunch of water bottles, some soda, cheese sticks, gogurt and a couple other small things and it was so great!! Could have probablly put more milk in too if needed.
Have fun!!