Ditto, on the idea of a "Pocket Shower" type solution. Any collapsible bag that's waterproof can hold an amount of water tied above your head on a tree branch (or whatever), and then a bit of biodegradable soap and a good handcloth for washing down.
Doesn't work well if it's cold enough to freeze all the water before use, but otherwise it's a good way to go about it.
Worst case, I've been able to wet a handcloth (~10x20" size or so), wipe down, then squeeze out the towel. Not quite as good as a "shower" from the hanging water source, but a good second-place choice.