It depends on the year, really. A few years ago there was a bad 2 weeks that knocked out power to about 200,000 households around the Columbus area. Ice accumulated on poles and trees and turned a limb with a 1 inch circumference into a limb with a 4 or 5 inch circumference.
It does snow here every winter, and my yard will be completely covered during the snow falls... then a little will melt and it'll happen again. Any water will freeze.