Michigan DNR wants to kill all Mute Swans in order to introduce the larger Trumpeter Swans for Trophy Waterfowl hunting purposes. So, they are not going to help nor will they allow anyone else in a local or state capacity. If the swan dies, it will be one less one they have to deal with. And, yes, swans and other waterfowl can become frozen in the ice.

So, you will need to safely access the ice with a boat or other safety rescue device and unfreeze the swan from the ice. If the swan stays frozen, it will die from exposure, drowning, starvation, dehydration or predation as predators can attack the swan on the ice. The swan needs to be freed quickly, but human rescuers must be cautious of not falling through things ice. The Regal Swan