Hibernate.
Actually, this is a re-curring story; it has been reported in the past.
Gators allow the ice to form around their head while their nose is above water, assuring they will breathe.
Their heart stays in liquid water (warmer than freezing) and they simply stop moving until the water thaws. They aren’t really “hibernating” or sleeping.
Think of it this way, most folks who fall through the ice usually die from drowning because they can’t back-track to the hole and can’t break the ice from below.
See my 1691.