Might as well leave it there....it'll be snowing again in a couple of months.

J/K
Salt stains, as you probably know, are caused by road (rock) salt having/containing calcium chloride and magnesium chloride. Difficulties in removing these road salt stains from carpet/fabric arise because of their solubility. (When left too long, road salt stains may form calcium carbonate deposits on the carpet/fabric fibers... and it is mildly/quite insoluble).
First step is to take a fairly stiff brush to expel/loosen as much road salt from the carpet fibers as you can. Remove as much of this debris as possible with a vacuum cleaner.
Then spray the road salt stained areas with a
mixture of: Cool-to-warm-water/carpet cleaner (Folex, properly diluted, for example) and allow it enough dwell time to soak-in and start dissolving the salt stains. These road salt stains become highly alkaline, once mixed with water, and are highly corrosive. {You'll need something acidic to neutralize the salt stains.} Using a
white cloth (a
white MF is an excellent choice)
Blot,
do not scrub, (scrubbing can drive the road salt briny solution further down into the carpet's fibers) with a rinse solution of 50/50 vinegar and water. This will help neutralize the road salt stain's briny solution, as referrenced above. You may have to repeat this process (maybe several times) to remove the vast majority (hopefully all) of the salt stains. The proverbial: "Patience is a Virtue" is most apt in this situation. That, and a lot of rinse cycles.
For the next step, clean the entire carpet area with your choice of carpet shampoo and rinse. If you don't have a carpet extractor, take your wet/dry vacuum and remove as much of the excess water as you can. Then
Totally Drying the carpet is imperative. If not...any road salt that would happen to be left behind would react with any moisture in the carpet and become corrosive again.
For the final step, I'd suggest applying a carpet/fabric protection such as 303 Fabric Guard, once the carpet has dried completely. This will aid in the next round of spring-time road salt clean-up.
Just a few ideas I had. Hope they are of some help.
Bob