According to Cool Antarctica, penguins survive in Antarctica thanks to their thick layer of subcutaneous fat and their small surface-volume ratio. These are essential to maintaining the penguins' core temperature while the animals are submerged in freezing water. Penguins also have feathers, and air trapped between them helps the birds stay warm while on land.
Penguins' feathers are ineffective insulators in water and strong winds. However, they help penguins shed water and dry quickly. When penguins need extra insulation, they ripple the muscles beneath their skin, puffing the feathers out and trapping additional air between them. Once warmed by the penguins' body heat, the air provides additional insulation.
The Australian Antarctic Division of the Australian Government Department of the Environment reveals that Emperor penguins practice huddling, an important behavior that distributes body heat throughout a large group of penguins. This helps them stay warm while inactive. Other penguin species do not huddle because of their strong territorial instincts.
Penguins depend on their flippers and feet for their swimming ability, so those parts must be functional even in frigid water. The muscles that control them are not in the extremities themselves, but in the fat-insulated trunk of the body. This keeps the muscles warm enough to operate at all times and prevents penguins from drowning due to frozen flippers and feet.
Penguins also use their feet and flippers for cooling. These are the only parts of their bodies not covered in feathers. Exposing the feet and flippers to chilly air or cold water quickly cools those areas, which is effective when the penguin feels overheated.