Perniosis (a.k.a. Chilblains) is a seasonal condition triggered by prolonged exposure to cold and humidity. It typically affects the toes ( though also the lower legs, hands, ears and face ) where inflammation of the small blood vessels lead to painful, itchy, tender, skin injuries.
It typically appears 12-24 hours after exposure to cold and usually last for two to three weeks.
Although some instances of perniosis can be atlributed to the effects of other diseases (Raynaud's disease, erythromelalgia, lupus etc) the common type. which is related to cold exposure, has biophysical mechanisms that have not yet been fully explained.
One hypothesis is that the cold causes small blood vessels to contract, and that this can lead to oxygen deficiency and cell damage - but the exact mechanism is currently unknown.
Further information UK NHS