Your problem can be Raynauds, an inmune disease (some cause disturbances in the blood and vessels when they are exposed to cold) or very likely too neuropathy. If your disorder is located only in one or two fingers, neuropathy could be the cause.

A common cause of this kind of neuropathies is a drug induced reaction. There are dozens of drugs known to cause these symptoms like lariam (antimalarian), quinolones (widely used antibiotics like cipro, levaquin), neuroleptics, inmune supressors, and many more. In many cases symptoms appear well after ending the treatment of the offending drug (months later).

You should check for the list of drugs taken up to a year before the onset of your symptoms and refer to a neurologist and a rheumatologist.