"I wear an overcoat in the winter." (more common)

or

"In the winter, I wear an overcoat." (also correct)

It's Hautis' sentence so, except for extreme circumstances, he gets to decide. However it doesn't seem that bad as it is now to me.

It's Hautis's sentence, but "in winter" doesn't sound right without the article...

I mean, it's occasionally used as a (somewhat poetic) adjective (e.g. 'The Lion in Winter'). But in everyday speech you wouldn't say, f.e., "In winter, I like to go skiing".

What about if it was the other way around?

　　I wear an overcoat in winter.

If you still think that's odd then I think we'll have to agree to disagree. Not everybody speaks the _same_ English, after all.

I hereby agree to the agreement of disagreement. I feel like if a high school English teacher saw that sentence, she would put the little triangle and add the "the". At least, in the U.S.. I suppose that in Britain they might be more poetic, and it is the British flag here after all...

Yeah, actually hits sounds a little like the "Go to (the) hospital" disagreement. British English (A.K.A. English Squared, A.K.A. English ;-) doesn't require the 'the' when you go to hospital, but American English does.

Shouldn't we add a comma?
In winter, I wear an overcoat.