I've heard that if your skin is too clean you are more prone to frost-bite. More precisely I think you want to get rid of the dirt, but stay greasy. I think hot water does 99% of the work, so I've never bothered with any soap. Sweating from daily exercise and hot water should be enough, most of the time. An alcohol and water splash as aftershave and under the arms and crotch feels pretty good. I do that at home with a capful of cheap gin. Doesn't cost that much more than aftershave and its a little more pure. The snow bath thing isn't that bad if your all fired up and do only half your body at a time.

I like phats idea of using a sock or whatever your washing as the sponge. Rinse it in cold water first to get most of the dirt out, then drop it in a pot of boiling water from the Kelly Kettle. Let it soak until its cooled enough to handle. Use it for your sponge bath, then rinse it again and squeeze it out and them figure out how your going to dry it. Drying socks or underwear is the tricky part. I think its easiest to dry stuff with a fire while wearing it. On a dry sunny day you can wear socks as mitts, and sometimes you can put your long underwear tops or bottoms on squeezed dried and wear extra clothing on the other half and hike or ski that way until dry. I don't bring extra clothes, just lots of clothes enough to wear all at once for the worst conditions broken down into layers. I find extra layers just get wet and stay that way, but enough clothes for the worst is manageable. Wool for what stays on mostly, and synthetics for the rest.