Other cause possible. Raynaud's phenomenon is a well known cause of cold hands and feet due to spasm of blood vessels supplying blood to the hands or feet. Other conditions can decrease blood flow to the extremities, leading to cold hands and feet. A primary care doctor can evaluate for anemia, peripheral artery disease, hormonal imbalances, autoimmune disorders, smoking (nicotine), drug side effects, etc...
Appearance and temp. Raynaud's classically white-pale with spasm, cyanosis-blue with congestion and deoxygenation, and rubor-red with post spasm vasodilation. Cold exposure oh hands - to ice cube or cold drink even in swarm place may induce and is basis for testing. Cold feet are likely cold! But can be from vascular obstruction or embolism.
Yes. It is a disease associated with micro (small) vessels of your toes and fingers. When your feet are exposed to cold they constrict and you get cold toes and tingling sensation in your toes. Try to cover the your toes up at all times.