It happened to me twice last winter. BMW NA was completely useless since my warranty expired. This problem is a safety hazard, since you can shut the doors by pulling the door shut, then pressing the lock button. Problem with that is you get locked in the car until the doors thaw. And the door isnt even completely latched shot. Piece of crap design.
The way this problem seems to happen is that when snow/ice melts on the windows, the water runs down into the door. If its still inside the door when you shut down and this water remains there long enough to freeze, then your screwed.
POSSIBLE SCENERIO: You run out one very cold night to the store. You park, come back out to your car and find the doors dont shut because with all the cold, the water in the door froze. Now you're stuck at night in a parking lot without doors. As bad as that sounds, now replace that scenerio with your wife and small child being stuck one cold night in a parking lot and cant shut the doors. I would send BMW a threatening legal letter (my wife's an attorney, so its free).
I really see a lawsuit looming for BMW because this is clearly a defective design in the doors.
BMW needs to step up and recall these particular models because if they cant figure out how to shut a f****n door, I will never purchase another BMW again (I'm on my third and last).