From the Mayo clinic website:
Chilblains
Chilblains are the painful inflammation of small blood vessels in your skin that occur in response to sudden warming from cold temperatures. Also known as pernio, chilblains can cause itching, red patches, swelling and blistering on extremities, such as on your toes, fingers, ears and nose.
Chilblains usually respond well to treatment and clear up within one to three weeks, though they may recur seasonally for years. Treatments typically consist of lotions and medication. While Chilblains don't usually result in permanent injury, they can lead to infection, which may cause severe damage if left untreated.
The best approach to chilblains is to avoid developing them by limiting your exposure to cold, dressing warmly and covering exposed skin.