I used to have a mk2 golf that did that. It was strictly a cold weather thing. Never did fix it before I sold it. The one thing that comes to mind is the thermoswitch in the intake that senses when the temp drops.
What is is meant to do is let vacuum to the air plate under the air filter (in the air box) That plate then shuts off the air intake from outside and opens the air intake from behind the exhaust manifold.
If you have a break in the vacuum line going from the thermoswitch to that air plate then the thermoswitch is atually just opening a good size vacuum leak, which will make your idle go crazy and f*** with your fuel air mixture. That would also account for the problem only happening in the cold weather.