I live in Illinois and have never found the carpet stains left from road chemicals to be permanent, but they are a little more difficult to clean than a rubber mat.
The road chemicals are designed to resist being diluted with plain water. Using a scrub brush with a mixture of 50% water and 50% white vinegar in a spray bottle will dilute the chemicals enough that you can shop vac the stain out of the carpet. Follow up with carpet cleaner to remove the vinegar smell.
Even my rubber mats get stained by the chemicals in my state.
Not sure what mix they use on the roads, or also at businesses.
It appears to be like a white stain.
I tried vinegar, degreaser, and some other stuff then gave up, it just for my feet anyways.
But fabric gets hard and ruined in the winter so even if it's cleaned you can see where you put your foot as it's run down to the bottom, kinda hard to explain. Almost looks like a flat plastic floor mat by the time the carpet goes through 1 or 2 winters. The Limited mats should hold up better because of the material they are made of, but salt other stuff will get into it pretty good.
I sold my Limited's floor mats for $450 and bought Husky all weathers for $125 but to each their own.