There is a Summer / Autumn / Winter / Spring pattern in the Temperate zone, also affecting the Desert and the Grassland climatic zones and, a Wet / Dry pattern in the tropical north which includes the Equatorial, Tropical and sub-tropical zones.
Most likely, your lips are suffering from excessive dryness, or chapping. Actually, picking at them and peeling off the skin can worsen the situation, as this can make the dryness worse. It would be better to try applying a good lip balm or lip moisturizing lotion. This should help you break the cycle of dryness and peeling, but only if you can refrain from picking at the skin in the meantime.
Jan 6. Winter is a hard time for every skin type, whether you're dry or oily. The outdoor air combined with the indoor heat can dehydrate our skin and cause lips to crack, bleed, and peel. Many of us shrug off chapped lips as par for the course, but really, they can be a sign of more significant health issues.