Welcome AA,
I just got back from Europe where I had 30+ degree F temp changes. It was the first time I had to deal with that particular challenge.
Opting out of formals isn't for me. So, I simply thought out carefully what would work for daytime excursions, my night garb is easy. Since you are going to Anarctica, you won't have the problem I did. I had to make sure my daytime apparel was as "cosmopolitan" as my ports were. No jeans and sneaks in the Med for me. I prefer to dress like the locals.
Anyway, you'll have it easy. Just pack lots of layered clothing as Bob suggested, casual for day and decide how dressed up you'd like to get at night. I prefer to dress each evening and only do "smart casual" on first and last nights. However, you could wear khakis every night too, and that would be fine.
My advice to women is always the advice I give myself. Pack what you feel GOOD in and don't forget the Spanx! 
Oh, and one more thing. I never worry about needing something warmer than I packed, as Bob can attest, you can always pick up a nice hoodie, zip up coat and rain gear in the shops on board. Too hot? No problemo, t-shirts and casual short sleeves galore. Formal wear for women also has a good selection on M Class. Lots of various formal separates, bags, jewlery, etc. Not so much for men...they'd rather rent anyway.
