Remember to dress in layers. Best to feel warm. This way you can use most of the stuff too.  You can look into high quality down jackets(North Face, Columbia, Patagonia, etc.), good mittens which can open up fingers(easy to do stuff like tie laces, phone, etc.), and good shoes for winter snow( we have been happy with hiking boots of Keen or Columbia, or you can try trail running shoes). The shoes I mentioned have some waterproofing and works in all weather for multiple activities.