Good you seem to have it. I have gotten too old to enjoy working outside in the cold. Come to think of it age is not a requirement either.
Multiple plug failure in cold weather is really not all that strange. Probably at least one has been burnt out for a little while anyways.
Usually I do not replace all the plugs if only one fails. In your case a complete new set might be worthwhile. Do not buy an inferior brand. Buy bosh or beru. Usually money well spent.
Mercedes are about the only cars I have owned that faults seem to correct themselves sometimes. Best of luck on the electrical thing.