A change in the weather often results in a change in one's skin, as well as, one's beauty routine. Things are different. You're different. With the colder -and windier- winter weather comes drier skin. It's no longer humid out, depending on where you're living. If your skin changes, some of the products you've been using will no longer work. You can't use items for oily skin when you no longer have oily skin. Moreover, a lot of beauty trends change. For example, it's unlikely that people will wear lighter pinks or coral lipsticks during the winter.
Chapstick.
Colder weather usually means chapped lips. I don't want cracked, bleeding, crusty lips so I always keep my chapstick within reach. I personally prefer either Burt Bee's or Vaseline. I know Vaseline isn't a chapstick but it does wonders for your lips!
Moisturizer.
Cold weather equates to drier weather, which means dry/drier skin. I always increase the amount of moisturizer during the months so that my skin won't get too dry. Sometimes, I'll switch to a cream moisturizer, since I use a gel moisturizer, around the drier parts of my face.
Liquid/Cream Foundation.
Since you're more likely to have drier skin during the colder months, you don't want a powder foundation to make your skin look dry.
Face mask.
Face masks are the best way to treat dry skin during the winter! Obviously, clay masks may not be the best option, but there are several moisturizing sheet masks or gel masks out there!
Blush.
This may seem like a stupid "necessity" but it's perfect for warming up your face! Most people are much paler during the winter, obviously, and blush helps you look less washed-out.