Well, how cold are we speaking? And what kind of trip? will you be spending a lot of time outdoors?
Below is what I usually wear on cold winter days (which also served me well for Christmas in the Scottish highlands, to give you a frame of reference). but I wouldn’t wear those if I’d go skiing or holidayed in northern Scandinavia…
it also depends on whether it’s still warm enough to rain!
Long, warm coat.
Warm, waterproof shoes (at least ankle height) with good isolation (not just the lining but also the soles.
Good thermals. I prefer natural wool fibre but some people have sensitive skin.
If you’re partial to jeans (whether that’s feasible really depends on the amount of time you spend outside and the temperatures): make sure you can comfortable fit thermals - or at the very least tights - underneath. (Although you won
something for your head that you’ll actually wear. I usually prefer a headband (even though it’s not quite as warm as a had) because it won’t mess up my hair too much.
gloves / mittens. I often wear wrist warmers around the office…
good socks! (Not cotton.)
Invest in layers.
Make sure you can actually combine the items of clothing. A bulky scarf with a high neck-jacket or coat won’t really work.
sunglasses and sunscreen may be a necessity (depends on your destination).
I personally prefer natural fibres such as wool or cashmere. But polyester blends are fine as well imo. Just don’t wear cotton jumpers or items of clothing, even if they’re thick or have lining.