If the lake is freshwater, then the swans can do just fine. The three types of white swans in Michigan would be the Trumpeter Swans, Tundra Swans and Mute Swans. Did you notice the color of the beaks? If so, this would provide a good identification for the species. Black beaks would be Trumpeter, black beak with small yellow coloration near the eye (lore) (this would probably not be the species because this is a fairly small swan in relation to the other species+, or orange beak would be the Mute Swan.

If they were extremely large swans, they would probably be the Trumpeter Swans which are the largest of the swan species. The Regal Swan