No. This common cold weather myth likely comes from an old study that measured heat loss from individuals wearing arctic survival suits but no hats. Since it was the only body part that wasn’t insulated that’s where most heat loss occurred. If you go out in the cold with any body part uncovered you will lose more heat from that part. So keeping your head and face covered is as important as keeping the rest of you covered in cold temperatures.
Vreeman, R. C. & Carroll, A. E. (2008). Festive medical myths. The BMJ. DOI:10.1136/bmj.a2769