HHMMM
Several points of contention here!
FIRST PRIORIty
OP: GO SEE YOUR DOCTOR! IF there is NO medical reason, simply WEAR GLOVES as often as you need to!
1} HYPO and HYPER glycemia ARE two different things, but HypO {low sugar} is what is called "pre-diabetic state"...I know I was one for 20 some years, always being considered pre-diabetic. WHY? because as someone here noted it can LEAD to "adult onset diabetes", AKA "Type 2 Diabetes" {high sugar}. Now I am diabetic! ANd my FEET, not my hands, are the COLD CULPRIT. They are like icicles at below 50 degreesF. Poor circulation in the extremities is one problem with diabetes. I simply wear 2 pairs of sock, one regular and one merino wool and always wear fuzzy lined slippers or shoes to keep my feet warm.
2}as noted the OP is a small person weighing little. THAT may be her problem, medical causes aside.
3} I strip to a t-shirt in colder weather when I work up a sweat. I am also overweight and even down in the 20s will wear a long sleeve shirt, a sweater and my LIGHT SPRING jacket ONLY. {my feet are bundled of course.}
If I start to sweat a lot, I take one or more off. SO People CAN wear a t-shirt or thin long sleeve shirt in colder weather, WITHOUT BS-ing anyone! HEck I see guys {usually} in shorts in the twenties as normal attire,and lets not forget the ladies whose only covering is a short skirt over pantyhose. Like my feet, though my legs get cold easier than my torso, so I stop wearing shorts around 40.
I DO wear a light insulated winter jacket in the teens and below and wear gloves until the vehicle heats up OR all the time if outside. I'm not stupid. But I take it OFF in the stores, any heated building or I start to sweat! But I will make the journey to get the mail without jacket and gloves, even in the single digits and not think a thing of it. I also wear a hat of some kind ALL THE TIME.. In summer the ventilated kind with a sweat band to keep it from dripping in my eyes, in the winter a warmer one, and in rain a wet-tolerant one.
It's all about ONE'S LEVEL OF COMFORT. What's cold gets covered, what's hot gets uncovered.
AND some people ARE "COLD TOLERANT" And others "HEAT TOLERANT". SA a former chef in restaurants {glorified line cook}, My hands are not so sensitive to heat that I cannot reach in grab something sauteeing or bubbling in fry oil! BUt...there IS a limit to what heat my fingers and hands can tolerate without burning them! ESpecially how LONG I can handle something THAT HOT. Iff you burn your hands, quickly douse in COLD water and ICE as soon as possible.