Bidirectional dedicated bike paths are usually at least car-sized. They will fit a regular plow just fine. Monodirectional bike lanes usually lack separation from the rest of the road, so they get plowed for free as a side-effect of plowing the car lane.
In the city where I live (which is _usually_ pretty bike friendly) the plow moves the snow from the car lanes onto the bike lanes a lot of the time :/