I have wondered about that myself but never tried it. I usually just "damp mop" them with a bucket of water and cloth. I know they make a waterless shampoo for horses and I heard a suggestion on here on another thread about using a brush dipped in water too. I have used cowboy magic spot remover and it works pretty good on doing poo spots. Vida is black so I don't worry about it as much as when I had a grey/white horse.
Unless someone else said it to, it was me who said about dipping the brush in water thing :) this is a really good way but if you are worried about her getting wet and chilled you could try a damp cloth. Sometimes in winter I get an old tea towel, wet it and leave it to dry until its just damp or almost dry but not quite. This is good for removing dust and general muck.
Other than that, there are a number of excellent dry shampoos as mentioned by vida
For showmanship and in hand classes we put baby powder right on our horses socks. If we can do it on that part of their body then I don't see what the problem would be with applying it to any other place. We only use it to get the white parts whiter.
Well it has been some time since I posted this and I've thought about it. I've decided I shouldn't do it because it'll remove the natural oils that protect her against bad weather. And since I turn her out without a blanket (she's unclipped btw) that probably wouldn't be a good thing. So I think I'll just have to live with her being dirty until it warms up enough so I don't have to worry about the snow and rain soaking her to the bone. But thanks for the input anyway.