Hypothermia can happen in most mammals in cold weather and can be fatal. Baby mammals such as kittens are unable to regulate their body temperatures and have a risk of hypothermia if they are not kept warm by their mothers. 
Many animals other than humans often induce hypothermia during hibernation or torpor.
Water bears (Tardigrade), microscopic multicellular organisms, can survive freezing at low temperatures by replacing most of their internal water with the sugar trehalose, preventing the crystallization that otherwise damages cell membranes.