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.
Use a humidifier to moisturize the air in your home and apply shea butter or Vaseline on your lips. Read More. If you peel this dry skin, the healing process starts all over again with dry skin on your lip. Dehydration is the commonest cause of dry cracked lips. Drink plenty of water and see. The other possibility is iron and Vit B deficiency. A lip balm preferably petroleum jelly, Vit B supplements, iron, and honey should help. They can also be caused by allergies and infections.