Don’t have vinegar? You could use dishwashing detergent, but it probably won’t be as effective. There’s also carpet shampoos and salt cleaners, but if you had those, you probably wouldn’t be on this page.
If you have a scrubbing brush, you could use it at this point if you’d like. You want to do it delicately, however; the aim is to stir up the salt, not to dig it in deeper. Just lightly scrub the carpet, stirring the stain to the surface.
You could also finish the job off with a wet/dry vacuum. Just dab the towel on the area, pull out your vacuum, and start sucking up the salt stain. This is a good method for the smell, too. If the stain looms, repeat the process a few times. Salt can be stubborn, but it’s definitely removable. If vinegar doesn’t work (with a few applications, it should), look into a product that is specifically designed for road salt removal.
If it’s your floor mats that are the culprit, remove them and hang them to dry (just make sure you don’t get new salt stains underneath them!). If the stains are on an area that you can’t remove, roll your windows down and air out the car.