When your hands or feet (and sometimes other parts of the body, especially your ears and nose) get too cold, they can be injured or react in different ways.
The most severe cold injury is frostbite, which is true tissue freezing (ice crystals form in the skin and other tissues of the body). Frostbite causes permanent damage to blood vessels and other structures. Frostnip is also ice crystal formation in tissues but only in the very outer layer of the skin. It causes no permanent damage.
Immersion injury results from exposure of wet feet (or hands) to cold temperatures at or above freezing. It develops over hours to days and damages the nerves and muscles. Like frostbite, immersion injury causes permanent damage.
Other conditions of cold hands or feet are pernio, Raynaud's phenomenon, cryoglobulin formation, and cold urticaria.