Removing Road Salt
Use a stiff brush to dislodge any loose road salt and then remove with a vacuum, spray the area with a carpet cleaner and let it soak in, the salt stains are highly alkaline once mixed with water, so I'd reach for an acidic product to counteract/neutralize. You might find that rinsing with a solution of vinegar /water helps. Repeat until most of the stain has been lifted.
Finally clean carpets by spraying the area with a carpet shampoo rinse and then remove with a carpet extractor. Using the vacuum, remove the excess moisture, loose dirt and the grime, allow carpets / mats to thoroughly dry before use, and then apply a fabric protection (303TM High Tech Fabric Guard) Be aware that once you add water to salt it becomes corrosive, so take care to dry the affected area thoroughly after the salt has been removed.