I just use dawn dish soap, a sponge and the hose in the front yard. I make sure they are dried out completely before allowing the lid to close and I store them unplugged always. If I have to put it away a little wet, I just put a piece of scrap wood or something between the cooler and lid so some air gets in there.
The rotomolded coolers clean a lot easier. That smoother, less textured surface goes pretty quickly.