A large number of diseases could cause such numbness, the commonest ones being:
Cervical disc lesion: This may be associated with pain in the neck and weakness of the arm.
Peripheral neuropathy: common conditions causing this are diabetes, Vit. B deficiency, etc.
Vascular insufficiency: Atherosclerosis of arteries, claudication, etc, may cause vascular insufficiency.
You should also remember some common causes which are also the most likely. It may be that you had sat in an odd position for some time putting pressure on your arm which is giving it now a pins and needles sensation. Coldness of the hands may also cause these symptoms.
I would suggest that you simply warm your hands and relax, in all probability it should go away soon enough. If the symptoms increase suddenly, and specially if it is in your left hand, you need to consult and ER because there is a chance that it could be from the heart. If the symptoms persist chronically for days, then you need to consult yor doctor or a neurologist if possible and get yourself checked up, you may need a CT or MRI of the brain and spinal column and tests for muscle conductivity and nerve velocity, etc. and other tests for peripheral neuropathy.
You may look up this site for a discussion on problems similar to yours: