This is a good question because there are many variables to this question. How cold is your winter? Does your pond completely freeze during the winter months? Do you have an aerator that will stop the freezing? How old are the cygnets? Can they survive the winter without the parents, i.e., from predators, the inclement weather, etc., which would mandate that you would need to bring them indoors?
Were the parents pinioned? Were the parents wild swans? Did the parents ever teach them to fly?

Any and all of these questions could lean toward staying or flying. There are no guarantees in this situation. If they were never taught how to fly, does not mean that they cannot figure it out, but if you are the sole source of their food and have been since their hatching, they would probably tend to stay with you and you would need to care for them during inclement winter weather. We hope this information is of benefit. The Regal Swan