Two layers of everything!
I don't know if you are wearing cycling shoes, the ones with cleats, those are murder for keeping your feet warm, because of the holes in the soles: overshoes are needed, but the cold will still come through the bottom.
I get quite hot on the bike, you might need more than two layers.
Top layer, pick windproof items, waterproof never really is that anyway, also you get the boil in the bag effect.
Cold wind: a buff or two are indispensable, fleecy ones the best.
Fleecy cap under your helmet if you wear one, if not under your woolly hat, as long as one item covers the ears.
Gloves and socks: any that you feel warm in, you can get very thin gloves to put underneath windproof/waterproof ones.
Waterproof socks are great, they work, but they are not warm, I wear a thinner pair underneath in minus temperatures.
You can wear anything, does not need to be cycling specific, walking and running gear work fine.
Tbh, many times I've bought a cycling specific item, to find out that it has not been as warm or as comfy as the same item marketed for general outdoor use.