The National Climatic Data Center has a web page that generates the snowfall climatology and extremes for any U.S. state except Hawaii (sorry).
Link: http://www.ncdc.noaa.gov/ussc/USSCAppController?action=map
From there you can pick a state and look at state-wide numbers like who had the greatest 1-day snowfall (24 inches at Coatsburg IL on Feb. 28, 1900) or the great snow depth (39 inches at Antioch on Jan. 16, 1979). You can also pull up more detailed station by station analysis of snowfall including averages and dates of the earliest and latest snowfall, etc.