Average winter snowfall over the State ranges from about inch per year on the Outer Banks and along the lower coast to about 10 inches in the northern Piedmont and 16 inches in the southern Mountains. Some of the higher mountain peaks and upper slopes receive an average of nearly 50 inches a year.
As far as somewhat populated areas, the northwestern section of the state is historically the snowiest. Think Watagua, Avery, Ashe and Mitchell counties along the NC/TN border. On the average over a 51 year period, the City of Boone recorded an average annual snowfall of 35.8".
Historical Climate Summaries for North Carolina | Welcome - Southeast Regional Climate Center