Last time I went backpacking I didn't think to bring any soap. I really missed it. Mostly I just scrubbed up with sand/gravel from the bottom of a little crick. Good enough for a woodsman I guess.

I had some dishes that were greasy with burnt spam & butter. Cold water and sand just won't take off the grease - it just smears it around. So, I mixed up some wood ashes with hot water to make a paste, smeared that all around the greasy pans and let them sit for a while. Cleaned the pans up good!

I think old time lye soap is just wood ashes and animal fat. I don't know the exact process or mixture but knowing the basics, I'm sure you could mix up something that would pass for soap. Man-o-man, that lye soap can burn you skin if you use it very often on sensitive areas.