Fix gears rule in the winter. I raced and rode out of Boston in the '70s, not owning a car. My beater fix gear was my winter workhorse (and 4 frame replacements later still is). On salt covered, often snowy or icy roads, the fix gear always worked and was easier to keep upright than any bike with a freewheel. Very much like a standard transmission car of the old days drove better on snow and ice than an automatic did. Other pluses: when the chain becomes so dry and salted that links start to freeze up, yo can just slide the rear wheel forward, get the chain slack right and ride. My rule was the three links frozen and it was time to do something but the bike was still rideable. When you are returning home tired n the dark, the bike is freezing cold and filthy, not having to attend to it to get it to work the next morning counts for a lot.
Another plus: downhills are a LOT warmer! Something you really appreciate when it is 10 degrees F.
Throw some cyclecross tires on your fix gear (or the biggest, softest tires you can fit) and try it.
Ben