Hi there ,
This sounds exactly like the symptoms of what I have. I have Raynauds Disease. I'll list some of the symptoms and you can see if it matches any of yours.
1)cold temperatures reduces blood supply to the extremities (and sometimes areas of skin) turning the skin pale/white and the area affected becomes cold and numb. (in my case this is hands and feet primarily , and my lower back somewhat bizarrely)
2) the affected area turns blue/purple when the oxygen in the blood lowers - it'll then start to look like a bruise that wont go away.
3) the change in skin tone/apparent bruising/coldness isnt permanent - when the affected areas warm up the blood flow will start again properly and the skin will go pinky/red before going back to normal. Sometimes my hands and feet/lower back will swell up and I'llg et awful pins and needles until its warmed up again.
Theres two different types of Raynauds - I have primary raynauds disease, this is where the symptoms are not related to any other disease , If your've been checked over by the Docter and he can't find a reason for your symptoms then It sounds to me like you could possibly have Raynauds disease too.
Secondary Raynauds - or Raynauds syndrome (different from raynauds disease) is where the symptoms are brought on by other illnesses , anorexia is a common one , and hypothyroidism as well as carpol tunnel.
Being in Scotland (it is when we travel back to the UK in winter that I flare up!!) you can't really escape the cold , but you can put on more layers to keep the areas warm , I always wear merino gloves and socks as well as big ski gloves and thick sheep wool boots to keep me warm , this lowers the symtoms.
I don't drink coffee as the caffine makes it worse - I avoid high caffine foods and drinks too , like soft drink and chocolate/sweets.
Theres not really alot you can do to treat it , as it isnt somthing that can be cured , but you can treat the symtoms by avoiding the coffee/cold.
I also take arnica tablets and have arnica cream which seems to help although I don't really know why. Flaxseed oil helps as well as cod liver oil which I take in pill form as it tastes foul. I use a stress ball when my hands are bad as the squeezing motion helps bring the blood flow back. Or rubbing the skin in circles quite vigoursly helps too.
Hope this info was helpful somewhat , if this sounds like what you might have PM me and I can tell you more about it.