I think many of your questions have been answered but I'll just add my 2 cents since I live in Ottawa.
For occasional use your winter tires should be fine, but if at any time your M2 becomes your winter DD I'd suggest something like Bridgestone Blizzaks or Michelin X-Ice. I DD'ed a 135i through 7 Ottawa winters, and now this is my 3rd winter with the M2, and I'm currently running X-Ice.
I don't visit this forum often anymore so if you'd like to reach out please PM me.
Welcome to Ottawa!
p.s. My first car was a 1991 BMW 318is! Loved that car