Standard cycling socks work best for temperatures above 40 degrees Fahrenheit. In colder temperatures riders should use wool cycling socks for warmth. Standard wool socks will be too thick for your cycling shoes. Make sure to get a quality sock that is extra thin for cycling applications.

Regular shoes don't hold up well in rain, mud, snow,  and ice. Off - road cycling shoes are made for the rough stuff. Don't use road shoes in snow, they have a smooth bottom which will make it difficult to keep your balance when off the bike. It is very likely that toes get cold in the super cold temps. The minimum required is a shoe cover that insulates your toes ( the first part of the foot that begins to freeze ). I like Castelli's Toe Thingy ( see below ), but there are many competing products. 

A complete thin shoe cover is nice for windy conditions. 

However a thick cover is required for long rides in the bitter cold.