If the swans are pinioned, meaning surgically rendered unable to fly because they are captive swans, then this would be one of the reasons that they do not fly. There are several other possibilities such as the young birds may not have their complete flight feathers yet, or they have lived in this area for so long that they understand how to stay alive in inclement winter weather.

If the birds are able to fly, the amount of open area for take-off may not be sufficient for them to leave.

Did the swans ever get free? Is there someone that you can call in the area that might be able to affect a rescue? The Regal Swan