Vacuums are your best friend!! I try to keep my horse as clean as possible in the winter because even though we have hot water in the barn, it gets cold here so we don't bath.
Basically I curry my horse twice a day (before and after my ride) making sure to take a long bristled brush over after to "flick" the dust off both times. I keep my horse blanketed while he is outside, and when it's colder I'll keep him blanketed in the barn with something breathable. It is actually healthier for the coat to be exposed than covered, so as long as he is in a clean stall he will be easier to groom without all the dander that builds up when he's blanketed all the time.
Another thing that is going to be your friend is miracle groom! It really helps get the dust out between vacuuming. I use it about once a week.
And for keeping his whites white, after regular grooming and removing all the dust from the stained area use a clean gel curry comb (http://images.orgill.com/200x200/1999374.JPG
) vigorously on it to get the stain out. A very small amount of green spot remover can also be used to lift the stain, then rub vigorously with a rag to get the spot remover off (hopefully with the spot!).