Warm up the inside layers before putting on your coat. Toss your sweater or the scarf in the dryer for a minute or 2. Your coat will help hold that heat in.
For me, wrapping myself up when I'm cold, just keeps the cold in.
My right hand that I broke recently is ice cold. I warm up a glove before putting it on. Then my brace. Otherwise, it's like keeping an ice cube from melting.