I don't understand. Do you sweat and still feel cold?

Almost. I typically sweat due to too much clothing, which results in me feeling cold.

What's weird about that? My armpits could be sweating (e.g., wearning a t-shirt + sweater) but my hands (no gloves) could be freezing.

Different parts of your body can feel hotter or colder, because the sensation of temperature is not about your internal body temp, but the heat transfer at the skin.

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.

If you would wear other kinds of clothes, you likely could be warm, but not sweat.

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.