Frostbite is damage to skin and flesh caused by extreme cold. The tissue actually freezes.
Fingers, toes, ears and the nose go first, since the body sacrifices its edges to protect the core. The early stage is numbness and white skin, and severe cases lead to amputation. Mountaineers and rough sleepers are the usual sufferers. The word is one word, and the adjective is frostbitten. It is quite separate from hypothermia, which is the core of the body cooling rather than the extremities freezing.
1nounfrostbiteInjury to body tissue caused by freezing.
“He lost two toes to frostbite.”
From frost + bite.
Etymology from Wiktionary, CC BY-SA