Exfoliating Cleansing Recommendations

Every winter, I get dry, flaky skin on my face, especially around my mouth and cheeks. It's actually kind of bothersome.
Even if I apply a generous amount of moisturizer before bed, I'm fine the next morning, but the dead skin starts flaking again from lunchtime onwards.
So I got some recommendations, and I heard the Vanilla Clean It Zero Original Cleansing Balm is pretty good. Has anyone tried this? I'm wondering if it has any exfoliating effects.
Also, this brand has a green container version. Which one would be better, the pink or the green one?