Carpets (front - floor) carpets wet.

I live in Ontario. Drive my Buick Century 2000 only short distance to work. (4 kilometers). I noticed that during winter season when the snow gets on shoes into front driver and pasanger side, the carpets are wet.
I am very careful to keep my feet only on the rubber mats, but the carpets are constantly wet. I tried to vacum the water out, blow/dry with air hose, that helped only for one day.
My question:
Could the water be coming in thru the front air vents? (The vents that are located in right and left corners, right under the windshield)?
I hate to go to the extreme and cut a section of carpets out so they can be taken out and dried!
It is hard to believe that the car designers would not think of this potential problem.. Any input on this?
Would beappreciated greatly !

I have a 98 Century that had a similar leak. The water was entering the passenger compartment from the cover over top of the cabin air filter. I ran a bead of rtv between the cover and the windshield. Havent had a leak since.

I have a 98 Century that had a similar leak. The water was entering the passenger compartment from the cover over top of the cabin air filter. I ran a bead of rtv between the cover and the windshield. Havent had a leak since.

Ditto. The gasket on the vent cover came loose on mine. Put it backon with RTV, no more water.