Someone posted a produce the other day that looks like it was made to order for the ice shack. It's called a Powerall and can be found on amazon. It's a little pricey @ $100 BUT they claim it's lithium battery is strong enough that it can jump start your car. The Powerall website shows them jumping a car and a LA city bus with it. It has a built in LED light, 2 USB outlets and ports to plug in jumper cables. Comes with a AC wall charger, DC power outlet charger, jumper cables, and USB cable with adapters for devices. It's 6.5"x2.9"x1.5" and weights 1 lbs, has a battery capacity of 12,000 mAH and jump start amps of 400 amps.
I'm seriously thinking of asking Santa to put one under the tree for me!