Shuddering/shaking At Cold Start

I have a 2000 A4 1.8t.

A few months ago, on the morning after first sub-freezing night of the fall, I had a problem starting it up. The engine turned over fine and I didn't need to crank it or anything, but it started shaking/shuddering as soon as it came on. The malfunction light flashed (because the engine hadn't idled, obviously) until I pumped the gas a few times, then it went off and the shuddering subsided.

I didn't bring the car in to have it checked out because the problem didn't reoccur...until today, the day after the first really, really cold night of the winter. This time the shaking/shuddering (not just a minor vibration, BTW - the whole car shook) went on for about 30 seconds to a minute of me revving the engine before it went away.

Anyone have any ideas what the problem here could be?