Try using a combination of a cream and gel based cleanser.
If you skin gets dry, normally a cream based cleanser (like Purity) will help moisturize, but you will also need to exfoliate about once or twice a week to remove excess dead skin. With oily skin, gel based cleansers help break down oil a bit faster than a cream based one as cream based cleansers take a bit longer to emulsify.
I love Anthony Logistics Gycolic Wash, it's a cream/gel combo with brightening, refreshing, and exfoliating glycolic acid. Which is just a fancy way to say fruit sugars which help to remove dead skin and impurities and the fruit sugars help to brighten and even out skin tone. It's a great way to exfoliate your skin without using a harsh, physical exfoliant that may scratch or be abrassive to your skin during such a delicate time with the weather changing.
If you do decide to use a physical exfoliant (one with particles you can feel), go for one with jojoba beads and gentle scrubbers, as opposed to sugar crystals, fruit seed powders, or salts, all of which have edges that can tear at skin. I love Boscia's Smoothing Facial Polish because it uses a sugar polymer to exfoliate, so you still get the sensation of something physically buffing your skin, but the particles are delicate and won't irritate.
Follow up with a day time moisturizer with at least an SPF 15, better if you can find a 30, that is oil free. CeraVe (availble at drug stores) is great because it's with SPF 30 but packs in humectants and ceramides to lock moisture in but won't add any greasy or heavy feel. They also make a night formula too. If you use a cream formula, stick to it at night time as it may be too heavy for day time use since you get oily in your t-zone.
