If you are in India ten i can say that this is due to the climate change which is taking place with the climate turning very cold and drying of the skin is evident, but there can be other reasons too like.
When dry skin is evident around your mouth, it could be more than just xerosis, or having naturally dry skin. If dry skin only appears around the oral area, it can be an indication of a skin condition called eczema, or dermatitis.