When it's cold, my fingers swell. What could be causing this?

Angio-edema. This is ussualy related to medication. Go over your list of meds with pharmacist and see if any have this side effect. Also reflex sympathetic dystrophy or also know as complex regional pain syndrome or causalgia can cause swelling on cold exposure.
Variety of things. Swelling can be caused by various causes. Blood clots can occur but also decreased activity can be the source of swelling. Check with your doctor.