Cars are enclosed spaces with poor air circulation when the car is not running. As a result, even a little bit of water on the carpet can lead to mildew and other problems if left alone. Cold, damp weather can make it even harder to get your car dry. Fortunately, a little heat and air circulation will do the trick.
Sop up as much water as you can with towels. If your carpet is really wet, hold down several towels on the carpet one at a time until they start coming up fairly dry.
Assess the temperature outside. If it is a warm, dry day with a good breeze, leave the windows down or the doors open with the car outside. This should dry it out fairly quickly.
Run the heater full blast with the heat coming out the floor vents. Crack the windows down about an inch. The heat will make the water evaporate, and the open windows will let the moisture leave the car.
Put the car in the garage. Leave the doors open and hook up some high-powered fans facing toward the carpet. Leave the fans running overnight if necessary.
If you leave the doors open, make sure the interior lights are off.