I’m sure that this has been pointed out, if your hands/leg/feet are cold, the blood vessels close to prevent further heat loss, vascular constriction, this is the way the body works to prevent heat loss. It slows down the rate at which you chill, the blood vessels in your head, don’t closes down, so heat loss keeps on happening until there is no heat left. (Death)
If it is cold enough to need gloves, it’s more important to wear a hat.
Take for example that you are dressed for the weather but:-
Wearing gloves and no hat, means you are actually increasing the amount of surface area that your body is trying to heat. (Both your hands and your head) so you will get colder slightly quicker
Wearing a hat and no gloves decreases the amount of surface area the body is trying to heat, as the hat helps retain body heat, and the blood vessels in your hands will constrict naturally to prevent heat loss.
Wearing a hat and gloves is the best option, providing you do not over heat and start sweating.
JMHO