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.
Peeling Inside Mouth. I have posted about the peeling inside my mouth before. I still have it and none of my doctors can tell me what is causing it. It is more behind the upper and lower lip than all over inside my mouth and more dead skin accumulates around the front and top teeth at night that anytime during the day. There are tiny tiny little bumps on the inside of my lower lip and it is tender when I brush my teeth.