the way I did it when I lived in upstate NY was to just shampoo the carpets. You can pre-treat them if it is real bad with some sort of carpet cleaner and hot water as was stated earlier and then just suck up the water with the shampooer.
As for the idea of salt getting to the metal, well, I wouldn't be worried about it now as it would have gotten there already when the snow and salt was brought in in the first place.
The best solution is get a beater. None of my stangs have seen snow. Parked from October to May every year. THat would be a large reason I am in louisiana
now...no more parking. If a beater isn't a option, get those floor mats that hold a lot of water. The heavy duty rubber ones. They will catch everything you bring in and then only the mat will get salty.
"When I know more, I'll be forthcoming. Or I won't be forthcoming, and I'll be honestly deceptive." - Les Miles