You know what happens to many bike lanes in winter around here (Germany)? The snow from the road gets heaped on them... It's usual for people to ride on the road then.
In fact in Copenhagen at least the bike lanes are cleared much more reliably than the road. The city owns many more of these bike lane snow-removal vehicles (which are small and fairly cheap) and only a few of the big road-plowing trucks. Salting the bicycle lanes also takes less salt, so tends to be done more readily.
But once enough snow accumulation has happened, a lost lane will be unavailable until spring. The dedicated bike path that cuts through my community is closed during the winter and much of the spring (too much snow accumulation). The snow plow budget in most years couldn't possibly cover it.