Six members of a family, including two children, were killed when an avalanche swept away their home late on Friday in the Banihal area, 110km south of Srinagar, the state capital, police said.
In the neighbouring area of Kapran, an avalanche killed another family of six.
In 2005, nearly 250 people were killed after heavy snowfall triggered avalanches that swept away hundreds of homes in southern Kashmir.
The Indian army, which has a large presence in the state, said it would airlift 1,500 people on Saturday who have been stranded for more than a week on a mountain highway that connects the Kashmir Valley with the rest of India.
In the state's high-altitude Ladakh region, thousands of goats that provide fine wool for Kashmir's famous Pashmina shawls are facing death as their winter pastures near the Chinese border have been covered by unexpected heavy snowfall.