Most birds have a special middle-ear receptor called the Vitali organ, which can sense incredibly small changes in barometric pressure. So if the activity at feeders suddenly becomes much more intense a storm may be approaching. Birds flying low or lining up on power lines also indicate swiftly falling air pressure.
During storms, birds may think of your feeder as a known source of food. While not dependent on feeders, it may make it easier for wild birds to brave a storm.
Even so winter storms can be hard on small birds like chickadees. In severe weather chickadees fly as little as possible to reduce the amount of heat lost though flight. It also helps if there are patches of dense vegetation or roosting boxes that give protection from the wind.