Great question. There are several reasons that swans bury their heads in their bodies. One is to sleep while feeling safe floating on the water. If they are cold, their warm feathers keep their bills, nose, ears and eyes warm and shielded from snow, rain or heavy wind. Their long necks can also be comfortably supported on their wings and they do not have to strain their necks by leaving them unsupported. The Regal Swan « Hide