I'm not convinced the typical segregated bike infrastructure is sufficiently segregated to be trusted to save me from 3,000 pounds of sliding steel. Certainly most of what we see in NYC isn't.
So in answer to the OP, winter is a time when I need to use discretion, and sometimes alter hours, or skip work on snow emergency days, or use public transit. However bike infrastructure wouldn't affect the decisions much except maybe at the fringes.
I commute to work because I enjoy it and it makes sense for me, not because I'm on any kind of mission. When it doesn't make sense, I don't take the bike.
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WARNING, I'm from New York. Thin skinned people should maintain safe distance.