Wool is nice and merino wool is the best.
Some synthetic stuff might also work, but is not so nice on the skin and some fiber just acts like a plastic sheet, meaning trapping all moisture inside.
But to repeat, we climbers and winter campers use merino wool. It is a bit more expensive, but worth it.
Hands with a pair of gloves on will feel colder than e.g. armpits under 3 layers of clothing. It's absolutely possible to sweat and still feel somewhat cold.
A little bit of sweat is normal, the problem comes, when this sweat cannot vaporate, but remain trapped inside your clothes.
Maybe try merino wool.
Check transpiration friendly clothing (I am missing the terminology right now) - the underware (and apparel) that you would wear while doing intensive sport. There exists fabric that attempts retention of heat and avoidance of sweating (and its cooling effect).
(By the way: as I tried searching for better terms, three instances, I met the following results, one per instance: 'transgender clothing'; 'see-through clothing'; 'the sexualization of women in sports'. The search engines algorithms are getting some fixation?)