stick to cycling specific clothing. some pants have proper liners and all you need is cycling shorts. I like my novara headwind pants. on bad winter days I wore snow pants made for sledding or skiiing, maybe a couple days I used a base layer under those.

for the top i used a cycling rain jacket and played with base layer and fleece shirt layering depending on temps.

for hands it was glove liner and loose fitting winter glove, sometimes with chemical hand warmers. not sure what I would do with brifters, those you can't operate with big gloves