My thoughts, though for sure, not definitive and not intended to substitute for what a doc might say, is that your fingers aren't getting enough oxygen and often oxygen is what the cells need for warmth.
Did you recently have trauma to your fingers (like a broken bone or cut?)? Could a ring on your finger be a bit too tight, therefore cutting off or decreasing the circulation to your fingers?
Certain thyroid conditions or nerve disorders can be culprits, too.
A much more extreme cause of this might be 'Raynaud's phenomenon.' I'd have something like this checked out by your doctor or other health practitioner. Hope you warm up!