We have "buffered" bike lanes and "protected" bike lanes in Chicago.
Buffered lanes are separated from traffic by painted lines, so theoretically they should be plowed at the same time as the traffic lanes. In my experience, they are left un-plowed about half the time.
Protected lanes are separated from traffic by (at least) a raised concrete curb, usually with plastic bollards. Some of these lanes also have parked cars between the raised curb/bollards and the traffic lanes... pretty good protection. Unfortunately, these lanes require a smaller snow plow to clear, and this doesn't happen as fast as might be wished.
In the case of either type of lane not being plowed, this means the cyclists are in the traffic lanes when the snow is too deep to ride through.
This past week I was *mostly* able to navigate the bike lanes, but had to take the traffic lane for a few blocks on one occasion. Most motorists seem to understand, as I didn't get honked at (or run over!).