I have always soaked my brushes and combs in a bucket of water, usually 3 gallons, with 2-3 teaspoons of bleach. Let them soak for an hour or so and then hose them out. If you have a garden spray attachment on your hose use the jet stream setting. It really gets the hair and dirt out of the hard and soft brushes.
^^^ Ditto, but if you have wooden handled brushes than try not to get the handles too wet. I fill my bathtub with a couple inches of water, and place the brushes brush-side down, along with some bleach and Listerine. After a while of soaking I rinse and scrub them, and then put them in front of a fan brush-side up to dry.
To keep the main dirt and dust off for a longer amount of time I just scrape them against the stall bars every now and then every time I groom.