The correct answer is option 2: Western Disturbances.

Western Disturbances are low-pressure systems that originate from the Mediterranean Sea and move eastwards across the northern parts of India, including the Kashmir region. These disturbances bring moisture from the Mediterranean Sea and result in enhanced precipitation over the Himalayan region, including Kashmir, especially during the winter months. The western disturbances interact with the cold air over the region and lead to snowfall in the higher altitudes of the Himalayas.

Option 1, South-west Monsoon, is not correct because the southwest monsoon primarily affects the Indian subcontinent during the summer months and is responsible for the majority of rainfall in the rest of India, but not in the winter season in Kashmir.

Option 3, Retreating Monsoon, refers to the withdrawal of the southwest monsoon from the Indian subcontinent and does not have a direct influence on the precipitation in the Kashmir region.

Option 4, Temperate Cyclone, is incorrect as well because while cyclones can bring heavy rainfall and snowfall to certain regions, they are not specifically associated with the winter precipitation in the Kashmir region.

Therefore, the correct answer is option 2: Western Disturbances.