Possible Clues:

• they can be made to rest in the water
• Aquatic animals
• Although all being on water, they get sore about a teetotaller
• Bewhiskered fauna
• One way to rest in the sea, perhaps
• River-dwelling mammals
• They live to rest in water
• Whiskered beasts
• Grown-up pups
• Sea mammals that float on their backs