Sure, stationary cycling can help maintain fitness, but it is boring. You ride and ride, but you don't get anywhere. Most cyclists will ride a trainer or rollers for up to one hour during the winter. The tradition is changing, though. We now do a mountain bike ride instead of a road ride.
Mountain bikes are slower than a road bike, and there is less wind-chill at a slower speed.
Being able to ride off-road is also an advantage because the trees provide shelter from the weather. Wide knobby tires also provide the traction needed for riding in the ice and snow. Usually I'll wear a toque under my helmet, a turtle neck sweater, a long-sleeve cycling jersey, a jacket, bike shorts, long johns, winter cycling tights, two pairs of socks, cycling shoes, cycling booties, and mittens. Sometimes it is too cold and snowy for cycling to be any fun, so it is a good idea to have an alternative activity. I love to run.