I would keep a cheap mtn bike with studded tires if you had to put all your eggs in one basket. I had several crashes on glare ice on my winter beater (with 700c road tires)-- I didn't have a mtn bike at the time. We tend to have much more ice than snow around here-- particularly heavy frost that freezes overnight, or freezing rain. It generally doesn't get very cold here (not much colder than freezing). We also have hills.

Riding fixed with road tires is good for clear, plowed roads-- but even then, you may encounter patches of snow or ice that are protected from the sun.

Hardcore posturing? Winter is a very relative term. I was always amused my the term "winter cycling jacket" when I lived in Minnesota. Winter could be well below zero (F or C)-- nothing like the climate the jacket was designed for. Road slicks are pretty much worthless on snow or ice. A few winters I went on a fixed winter ride in Mpls, and everyone crashed at least once.