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.
Cracked lips are a symptom in which the lips are dry, peeling or chapped. Breaks may appear on the surface, and the lips may become painful and may bleed. In most cases, cracked lips are not caused by a serious condition and do not pose any health risks. Common causes of cracked lips include dry or cold weather, sunburn, wind exposure, licking your lips, and breathing through your mouth. In some cases, mild conditions such as the common cold, dehydration, and nutritional deficiencies may also result in cracked lips.