Why would my hands, feet and other areas on my body get cold for no reason?

Could be Raynaud's: Raynaud's phenomenon is a symptom caused by constriction of small blood vessels, usually in the fingers and toes, leading to a lack of nutrients and oxygen going to the fingers and toes. Raynaud's phenomenon can be due to auto-immune disorders, hormonal imbalances, medication effects, etc... A primary care, endocrinology, or rheumatology doctor can look for raynaud's and other possible disorders.