Thinking of exploring Montreal for 10 days & NYE (Montréal)

I am thinking of visiting Montreal, I am having hard time finding blogs or other sites that talk about visiting in the winter months for New Years Eve. I have no idea what to expect beyond clear cold weather and some snow. But I would like to find out if possible in the next couple of days. Otherwise I am off to warm place like Miami or Honolulu.

I would like to know more about visiting in the winter, and is it safe to ride the underground at 11PM? or is it like NYC, where after 10PM it's bet to use a car service?

Can a woman walk to the store and not be bothered with stray cat calls?

I really have no clue, I have read that Montreal is safe. And to smart about traveling.
But after being in Costa Rica and Northern Canada. Safe could mean many things. So if a few of you living there could give me a heads up that would be wonderful.

I look forward to the dialogue.