My '06 A3 2.0T has a very noticeable cold draft coming from below the glove box. The draft can be felt by the driver's hand when using the gearshift. There is heat coming from the passengers floor vents (& all other vents). If you open the glove box it is very cold inside & the draft can be felt there as well. The driver side floor area has heat & there is no draft there. Any ideas?

 

Cabin air filter missing maybe?

 

Have an '06 A3 as well. Same thing happens. Noticable when it gets really cold out. So it's not just your vehicle. Probably a minor design flaw.

 

It is a small refrigerated area for keeping your pop cold!

I never noticed this on mine, I'll check it out.

 

2006 A3 - I have the same issue. I originally thought a vent hose was not put back correctly...or something was missing. I concur that it's a fault with the design.
If you press the recirculate button near the climate controls, the cold draft goes away. But look out for those fogged up windows if you keep the recirc on during the winter.