With the biting Arctic weather that we're experiencing, I would say my skin is more than just a little confused.  It knows it's oily, but is currently experiencing high levels of dehydration, and just cannot for the life of it figure out what today.  So I have brought in the big guns.  Balms.  Oils.  Moisture.
I am a sucker for a balm or oil cleanser.  The cleanse brought about by a balm or oil I feel is more intensive, and more cleanser-ish than an ordinary cleanser.  Don't get me wrong, I still use my Peaches and Clean every day, but I mix it up with a balm or oil.  I cleanse twice a day, and always, always, I cleanse twice within a cleanse.  Now, I do not skimp on time when cleansing - no matter what else is going on, just like with my make up routine, my cleanse is leisurely and effective.  My Cleansing Balm of choice is the Botanics, which has been my fave for a couple of years now (although very keen to try the Emma Hardie and Antipodes offerings), and my oil of choice in the Mac Cleanse-Off Oil which is just a miracle.  Both remove eye make up as well as the rest of my many layers of make up, but the balm requires a hot flannel cleanse to remove, whereas the oil emulsifies in hot water, and can be rinsed off.  
I generally use the Mac first as I can really scrub into my eyes with it, taking off the layers of eyeliner, and rinse it off, thereby not leaving great big black panda eye marks on my flannel!  
I then often go over with the balm, massaging it in, and flannelling off with super hot water.  Both have a lovely, calming scent, and leave the skin baby soft.
In terms of other oils, I really only use one - the Antipodes Avocado and Rosehip Oil, which I deem to be a multi-use miracle product.  Lately I have had a spot picking episode in which I practically gouged out my whole face, and this is the product I am relying on to heal the wound!  It leaves the skin soft and glowing, and smells like calm!
I hope this helps you with any wintery skin blues you may have!
Please feel free to leave any balm/oil suggestions and comments, I'd love to discover more!
Love A.x