My hands are always cold and blue. could it be due to a blocked artery?

Possibly: Cold and blue hands could definitely be due to a vascular problem. The three possibilities would be, 1) a blocked large artery of the arm, 2) a blocked vein in the arm causing venous congestion (blue color and swelling), or 3) a vasospastic condition of the hand called raynaud's phenomenon. Either way, the best test is an ultrasound. See someone urgently if you are having pain.

Get it checked: Dr. Aalami's answer is right on target. Although your hands could indicate a serious problem, they might also just be normal for you. Regardless, you want to get it checked out.