Is this a captive swan (pinioned and cannot fly) or a wild swan (capable of leaving and returning at will)?

If it is a captive swan, then this is probably why you are seeing it all winter long. It may not be able to migrate. Then, again, if it is a wild swan and your area or the swan's habitat has enough shelter to protect it against severe winter weather, then it might stay.

Is the habitat surrounded by lots of trees or buildings for shelter, free from predators, has open water provided by an aerator/de-icer, is the swan supplementally fed so that even if the resources in the pond are depleted during the winter months, the bird is still fed? Does it belong to someone and they are caring for it during the winter?

All of these questions need to be answered to determine if this is why the bird is staying or is able to survive in your area during winter months. Sorry we could not be of more assistance, but we need more information to determine the situation. The Regal Swan