This may certainly be true of wild swans as they may fly from pond to pond, especially during the migratory season to find appropriate food and nesting resources. However, once food and nesting is found, the swans are usually territorial and stay in the same vicinity. Swans will patrol their designated area and they will float on the pond, even when asleep. This may be the reason that they look like they are so restless.

Conversely, most swans (wild or captive) will settle down and will rest for hours at a time, bathing, preening or sleeping along the banks.

The verse also speaks of awakening and rising. The swans will become more active once dawn appears as they are more free to roam and swim without the threat of predators that are very prevalent at night, which is why most swans will sleep in the middle of the lake for protection. The Regal Swan