I would suggest that you go to see your primary care doctor
about this issue, especially since it has been persistent for several month and is actually associated with pain.
Although everyone's circulation is different, and it can be normal to have cool hands or feet, it is not normal for this to cause pain. There is something called Raynaud's phenomenon, which involve periodic clamping down of blood vessels in the hands or feet in response typically to exposure to cold temperatures; with this condition the fingers or toes will initially turn white or blue before circulation is restored. Although Raynaud's phenomenon is sometimes an isolated problem, it is often associated with an underlying connective tissue disorder and this will need to be ruled out by your doctor.
Another potential problem, if you are older and having diabetes, heart disease, or a similar medical problem, is a condition known as peripheral vascular disease. In this condition, the arteries leading to the feet become gradually clogged with cholesterol, which makes blood flow to the feet impaired, leading to pain or discomfort and coolness. This is also a condition which can be diagnosed by your primary care doctor, although it sometimes requires management by a vascular surgeon