Tips for travelling to a cold country?

Hi everyone, I’ve lived in Singapore my entire life and it’s my first time travelling to a cold place with subzero temps. I’m going to Northern Europe next year around Feb/March and have practically never stepped out of SEA 🤣

I’d love for any advice regarding clothing, shoes, skin and hair care from anyone who’ve travelled to places like that before!

The place I’m going would reach about -10 to -12 degrees at night and about -3 through the day, with strong winds as it’s a coastal region. I’ve already researched a bit and have some sort of idea on what to get, but no clue on where and what exactly to buy.

So far these are the things that I plan to buy based on my initial googling

1. Insulated inner wear
2. windproof Down Jacket / Parka
3. Snow shoes
4. Scarf and Beanie
5. good Lip balm and moisturiser

For my budget, I don’t exactly plan to buy super high end ones cuz realistically I don’t travel too much, much less to countries further out, but I’m also worried about low/bad quality stuff from shoppe and Taobao… Last thing I’d want is for me to freeze to death there and have to fork out extra money to buy stuff there

Thank you once again! I’ll reply and answer to as many questions as I can