My car does the same thing each time I turn the heat on. The scent comes straight from the vents. I just changed the cabin micro filter and I'll test it out in the am when it's cold again. If it still stinks, it's prob the evaporator core that needs to be flushed out (mildew). Infiniti in Mont. quoted me $170 for the service.
*Switch to fresh air approx 5-10 mins prior to stopping the engine to dry the moisture out from using the A/C.

 

I agree that the drain may be clogged, based on the location, it may not be easy to unclog it. If the leaves and debris are not cleaned from the vents under the wipers, that stuff can get into the HVAC ducts and rot causing the same type of odor.

I was amazed at the suction through those vents. I had turned the defroster on and out my hand over those vents, the "pull" is like a good vacuum cleaner.

 

Ozium in the returns and outer intakes worked for me. The outside air and heat and AC on for the last 5 minutes of a ride seems to help. Can anyone vouch for the value in a Charcoal OEM filter @ 70 bucks over an aftermarket 13 dollar plain in cabin filter?