Hit them with a stiff brush and a hose first.

Yes, that’s the real answer. Don’t overthink this.

Mud and salt are stubborn but not complicated. Let the mats dry completely — wet mats just smear everything around. Then take them outside, shake them out, and hit them with a stiff bristle brush to break up the caked-on mud. Hose them down thoroughly. If salt stains remain, mix a solution of white vinegar and warm water (about 1:1) and spray it on. Let it sit for a few minutes, scrub, rinse. Vinegar neutralizes road salt better than soap alone.

For rubber mats, you can skip the vinegar and just use a degreaser or dish soap. For carpeted mats, be careful not to soak them too much — they take forever to dry and can get musty if left wet in a cold garage. After rinsing, hang them or lay them flat in the sun. A wet vac speeds things up if you have one.

The real trick is doing this before the salt eats through the mat fibers. But since you’re already asking, you’re probably fine.