Is there anything effective for severe facial exfoliation during the dry season?

Hello. During this dry season, my biggest concern is none other than dead skin cells on my face. Even when I scrub or exfoliate, the relief is only temporary. My real worry is that white flakes of dead skin constantly appear around the wrinkles near my eyes and mouth—even in my daily life. Because of this, I can't wear makeup. It only becomes more noticeable when I do. My T-zone is oily while the rest of my face is dry, so I can't just apply oils carelessly. If I do, they flake off like dead skin. I keep my basic skincare routine simple, but if I use many steps, they flake off like dead skin. In today's busy world, I don't think applying just a toner and expecting it to absorb fully in ten minutes is realistic! The dead skin cells are a problem, but those areas also crack and feel stinging.