In addition to what others have said, I agree with Lena that it sounds a lot like Raynaud's. I have really horrible Raynaud's and my feet and legs "fall asleep" very easily because my blood isn't circulating properly. When you have Raynaud's your cells spasm when triggered by either cold or stress (or in my case, by nothing). This causes your feet to become very cold to the touch and often times change color. The most common color changing goes from blue to red to white (although it is not necessary to go through all 3 colors for it to be Raynaud's). Raynaud's tends to be harmless, but during the white stage it means that your feet are not getting enough blood as they need and you are more prone to lesions, etc. In terms of treatment it depends on how bad it is. I take Amlodipine (which is usually used to treat high blood pressure). It worked wonders at first, but has recently been working less and less.
I have never had a b12 deficiency, so trusting those above I think that you should definitely have your doctor do some blood work. There's no tests to diagnosis Raynaud's, it's more of a differential diagnosis and based off of symptoms.
Hope this was helpful!
Lupus, Secondary Raynaud's Phenomenon, Pernio (Chilblains)