Hi Naomi,
It sounds like you may have chilblains, my Father-in-law has the same problem and he was told by his consultant it was an autoimmune condition. His fingers go very painful, white and very cold and his fingers and hands all peel too, his nails are also very chipped and broken. He gets treatment for it but he suffers lots in the cold. He gets the thermal gloves to wear which help.
Hope this is a help.
Take care Lorna x