Could also be a clogged pick up. I had a similar problem on a 240D. It was so cold that the little bit of water I picked up froze onto the pick-up.

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1984 300Sd 210k

Former cars:
1984 300D 445k (!!) (Strider) Original (and not rebuilt) engine and transmission. Currently running on V80 ( 80% vegetable oil, 20% petroleum products). Actually not, taking a WVO break.
1993 300d 2.5 275k. Current 120/day commuter
1981 300SD 188k (Hans) Killed by a deer