I, too, like to hose or power wash stalls when weather allows.
If you can't, then I use a broom. First sweeping top down, then back to front. Even in the winter, if it is over 30F and a stall has filth on the walls, I'll use a broom and bucket of hot soapy detergent and scrub down the walls. I only do that, though, if I have another stall to put the horse in until its' stall is dried.