Recommendations for winter wear and accessories for travelling to Korea

Hi everyone, I have only ever travelled overseas in summer. I will be going to Korea in January 2025 and it will be my first ever winter trip. I absolutely hate the cold, and can barely survive even in Sydney winters sometimes. Thank goodness for Uniqlo heattech and puffers.

Could I please have some recommendations for the following items to stay warm in temperatures below 0:

• wool gloves - touch screen compatible would be amazing
• wool scarves
• wool socks
• beanies - what would be a warm beanie?
• shoes for winter - would sneakers be okay? How about Doc Martens? Or leather boots?
• leggings - fleece lined?
• any other clothing recommendations - tops, jackets, pants

I plan on buying one of all the above in Australia and getting the rest in Korea, however I need to have enough to at least survive the first day getting from the airport to the hotel!

Thank you in advance and happy new year!