Bathing your horse thoroughly with shampoo will get rid of the dust completely, at least for a little while! Only problem is, too frequent bathing strips out all of the natural oils and can dry out the skin and coat too much and then the coat will start to look and feel dull and dry. Remember, when you do decide to use shampoo, to rinse really well, any shampoo residue left in the coat can dry out the skin and leave a residue that will dull the coat and make your horse itchy and want to rub.
Hosing down with plain water after riding if your horse gets sweaty and if it is very hot out is a good idea and won't strip the oils from the skin and coat, I usually just wet the coat down well and then use a rubber curry of some sort, usually a rubber curry mitt, and then hose down once more and then scrape the excess water off.
For normal everyday grooming I just like to groom very thoroughly and get the skin and coat as clean as I can get it using lots of elbow grease. Rubber curry, natural bristle dandy brush, natural bristle oval/hand strap style body brush, very soft natural horsehair dandy or goat hair oval body brush or natural sheepskin mitt to finish off with. It helps to swipe the brushes across a metal curry every few strokes to keep the dirt from going back into the coat while you are grooming, also remember to knock the dirt out of the rubber curry every once in a while when using it.
As a few others have already mentioned finishing off a thorough grooming session with a damp wrung out towel or a microfibre mitt can help to remove any last traces of dust that the other grooming tools didn't get.