My personal opinion is that I wouldn't use a fixie in winter around here, although that may or may not be relevant depending on where you live. Even riding through 2-3 inches of snow that get put down over the pathways and roads overnight is not fun to ride through without being able to shift gear ratios. Its not outright difficult of course, but it does get tiring if you're riding in it for a while.

I would think that if you were needing to do the work on the bike anyways, why not go for something cheap and simple like a 3 speed internal? It would be fairly inexpensive, but give you more cadence control on the snow and have the same low maintenance.