This is much easier said than done. While it’s fun and easy to go accessory-free in the summer (since you’re wearing fewer pieces of clothing), over-accessorizing in winter can make you look like a “Sapin de Noël”, aka a Christmas tree. (Yes, it’s a saying.)
I rarely come across women wearing the full winter package in the streets of Paris (oversize beanies, knitted gloves, oversize scarves, furry boots). It’s just too much. Wear leather gloves (if it’s really very cold) with a turtleneck layered under a men’s coat to make you appear lighter and more French.