What can cause my hands, legs and feet to be blue and me be cold all the time?

Look further! . 'sluggish circulation' or 'not enough oxygen in blood' are two things that come to mind when somebody has bluish discoloration of hands and feet. If it happens only when you are exposed to cold you may have something called raynaud's disease. Beta blockers can cause spasm of blood vessels and make you feel cold. Causes are many. Please talk to your doctor.
May be benign. Given this is the winter, symptoms like these are often benign and fall within the range of normalcy, though it may be uncomfortable and cosmetically bothersome. However, you do need to make sure that your thyroid hormones are not low and that you may not have an underlying vascular (blood vessel) process going on (as benign as raynauds, or serious like peripheral arterial disease). See your md.