How large is the lake/bay? If you cannot safely access with a boat or other safety equipment, there is probably little that can be done. If the bay has even a little bit of water, then the swan may be able to survive until a larger area thaws.

If you can feed the swan and lure it onto the bank, you may be able to capture the bird with the help of a local wildlife rescue group. However, some states want the Mute Swans killed, so be careful that whomever you ask to help is in fact a no-kill shelter and not one where they will euthanize the bird.

The swan may have been caught in your bay during the latest inclement weather and either blown into the area or trapped so it could not leave. If the weather improves in the next few days, the bird should leave on its own accord. Wildlife will usually not stay in an area that entraps them so that they cannot get food or water.

However, if the bird continues to stay, and you cannot capture it, then it will have to fend for itself. If the bay or lake continues to be frozen, ultimately the bird could drown if it falls into the water and cannot get out, starve or a predator could get onto the ice and attack the bird. So, the best outcome would be for the weather to improve and the bird leave on its own accord. The Regal Swan