+1 Stephane. My own take is that if you are mentioning something like the weather, an emotional state, an article of clothing, a weapon, anything, it should have consequences in the story.
So yes, describing winter in your story does have consequences, a forgotten coat creates some hardship, a form of conflict that sustains interest in the story during a transition from pub to his home, that you chose to describe for some reason: perhaps a little world-building, or time to think or see something that has consequences later in the story.
However, all the consequences of winter can follow without further describing itself. There is a maxim in computer coding called DRY, meaning Don't Repeat Yourself, which applies to writing as well. Keep your story DRY!
If you are going to repeat yourself and keep telling people it is Winter, then each time you do that should have some consequence. Otherwise, you are treating the reader like a child by constantly reminding them of it. Tie those description to something that happens; even if the something is pretty minor, but if nothing else it can cause sensory or emotional reactions.
So YES and NO: I wouldn't mention it is winter every time he leaves the apartment. But the fact that it IS winter surely changes his behavior. He has to bundle up for winter; he is careful descending stone steps, he wears sneakers and thick socks, and keeps his office dress shoes and socks in his briefcase or a satchel. He has to walk around a dirty snowman on the sidewalk, he is wary of the icicles hanging off the porch overhang, and uses his umbrella to knock a few loose. Winter, ice and cold temperatures, should affect behavior (for everyone) and emotions; be it irritation or joy.
Pick some concrete consequence of the weather and describe it. "Winter" alone is vague and not concrete, you make it concrete through the specific conflicts or opportunities it inflicts or presents, respectively. Don't leave it up to the reader to guess what Winter is like for your characters, show them what it is like by how they deal with it.