Gem, TDs glasses/goggles advice is the best........ but..........
Ski socks are quite thin compared to walking socks and almost seemless. Not cheap but you can get away with one pair and some travel wash as they will be dry on the radiator by morning.
Same goes with a wickaway base layer, you might be surprised to find these are cheaper than the socks. T-shirts can be ok but keep them away from your skin
Hi Gem,
you go in Jan., can get cold - so don't spare on your equipment. You need sun glass ( uv) AND goggles ( for snow and bad weather ), something for your head ! and good ( waterproof ) gloves. Clothes; wear (more) layers, underwear, good socks !, (t-) shirt / (warm) sweater or fleece, wind-water proof jacket and pants.
You'll be fine up there ! have fun.
Nico