As a canadian, I find that unconvincing. For the last few years up until this July, my commute involved a 900m walk to the nearest subway stop (which I considered nice and short!) year-round. And yes, it took twice as long when there was 8-12" of fresh snow, which happened ib average every other week in winter.
Yeah, that sucks. If it takes you 12 minutes normally to walk 1 km (assuming 5 km/h, which is a normal walking speed), now it takes you 24 minutes to and from the station in the winter.
So you're spending 45 minutes a day just walking to and from the station. If the rest of your commute is 30 minutes (train + walking to work from train), you're commuting for nearly two hours (1:48) every day vs. 1:24 during the summer.
That's assuming you don't also walk slower from the train station to work, which would make it even more of a timesink.
If you lived right near the station, it would be 60 minutes every day, winter or summer.
I mean yeah, it's only an extra 30-60 minutes a day (and your point was really only about winter so we'll be fair and say 30 minutes a day), but shit, I'm not going to turn my nose up at that. I'd definitely pay a small premium to get that time back every single weekday.
In Montreal, I can count on the sidewalks being cleared well enough within 48 hours of a big storm and sort of cleared within 8h (< 2" snow, at least 16-20" wide path, basically one pass of the sidewalk plows.)
As I mentioned above, that's definitely not the case in the outer boroughs of New York (Manhattan in some cases too, depending on where you are, though I don't know that for certain).
There have been weeks at a time where I've had to walk in the street because the sidewalks were just inaccessible or sheets of ice, which makes proximity to the train station all the more important.
NYC gets a different kind of snow than Montreal. Plows just breeze through powder that hasn't been refrozen. Atlantic seaboard snow is a PITA to deal with.
City was Montreal.