Most people think a blizzard is when lots of snow falls, let's say one to two feet. That is often the case, but not always.
Blizzards are actually defined by a combination of snow, wind, visibility, and duration. There are three main criteria for a blizzard:
1) Snow or blowing snow
2) Winds in excess of 35 miles-per-hour
3) Visibility of 1/4 mile or less
If all three of those criteria are met for three or more consecutive hours, then it's officially a blizzard.
So the amount of snow doesn't determine a blizzard. In fact, a blizzard can be caused by an inch or two of snow significantly blowing around on the ground with strong winds and low visibility.