"Adult alligators can survive freezing conditions if they are in water. They submerge their body but keep their nostrils projecting above the water surface, so that when the surface freezes they can still breathe (called the "icing response") ... Yet another example of their amazing ability to survive."
Using this technique isn't the only way these creatures cope with the cold. Similar to hibernation in mammals, when temperatures drop, alligators enter into a state of brumation, wherein their metabolism slows as a way of preserving energy.
Fortunately, the alligators weren't under ice for too long.
On Tuesday, Shallotte River Swamp Park reported that the ice had thawed and the alligators were once again free.