The state that gets the most snow annually would be Alaska. The city of Valdez has an annual snow total of about 326 inches and many of the other towns and cities record high totals. Other states that receive a significant amount of snow include New Hampshire and New York. You can find more information here: http://nsidc.org/snow/facts.html
1 Additional Answer
The state that gets the most snow is Alaska. However, there are states such as Florida and Hawaii that do not see any snow except in rare circumstances. California, New Mexico and Arizona can see snow occasionally during winter months.