I've reposted this from the blog, hope you don't mind.
I generally use a handful of snow to get most of everything out, plus a tiny little plastic scraper. Give everything a scrub with a couple of handfuls of snow. Then I heat a cup of water, add some detergent, and starting with the least greasy plates, work my way through, tipping from dish to dish. I carry a pair of light weight dishwashing gloves to keep my hands dry, which makes it much more pleasant.
I also use them if I'm digging a snow platform, or pulling down a wet tent too. It means I'm happy to dry the tent off in the morning, since my hands aren't screaming at me.
I agree with Roger though, I never dry anything
I do this wherever I cook and eat. On a nice night this would be in an outside snow kitchen. If not, in the mid with no floor on my own, or the floor pulled back with the kids.
Last (first) snow trip with the kids there was an antechinus eating all the scrapings from our bowls. In the end he burrowed up from below our sump pit and would be sitting in the bottom of it waiting for breakfast!