Many of us on this site sleep in mittens/gloves. I sometimes put socks over my hands which are basically lightweight mittens. I don't like wearing "sleepwear" if I can help it, unless it's really cold. Mittens and a hat will definitely keep the chill off. Hats especially. Those are essentials for me.
About core temperature...I play disc golf often and when it's chilly, I wear an insulated vest. Down to about 45 deg. and light wind, my hands and arms don't get cold and are much freer to move. Very counter intuitive. I use to think vests were the most useless piece of fabric there was and now I wear one constantly in winter.

Your head, hands, and feet are big radiators, so it stands to reason your core temp can be kept higher if you cover them.