I wouldn't give up on cotton to quickly. Thin cotton and majority cotton blend banana hammocks are just not large or thick enough to seriously compromise cold weather performance.

back in the 70 the Navy saw flight crews showing up with burns from nylon and polyester underwear that melted into their skin. Their recommendation was to shift to majority natural fiber shorts. Silk works pretty well and it absorbs less moisture than cotton but most fliers went with cotton or cotton/poly blend shorts.

The reason is they are easily available, cheap, don't melt and while they do absorb some amount of moisture the thin cotton briefs, not to be confused with the thick white kids briefs, are so thin and small that the moisture held just isn't significant. They are also comfortable, don't chafe and don't get funky and permanently absorb the smell like many of the man made fibers do.

Quite a few mountaineers campers and soldiers have stuck with thin stretch cotton and cotton/poly blends even as are something of a compromise.