Hello
Try woolsocks, i myself cannot anymore wear synthetics, try wool,
for the cold now, go with a thin, for inner, and a bit thicker on top ( 2 layer princip). but if room is tight, go for one thick. I think icebreaker socks, and smartwool are very good. But if you have any wool, just try them first.
For me, and not being a expert, it seem synth gives some friction, so my apex of toes, get really red, and sore. also make sure that the sock is big enough, so it does not compress.
Cheers