How do you define that? Snow the most by weight within its boarders or the record for any one location? Most days with snow fall? Most days with snow on the ground?
In terms of tons, a large state with significant average snowfall, such as Montana, will probably have the most snow. I don't see any site that defines it by that measure. You could probably figure it out but it would take a while and a lot of time, data crunching, and topo maps.
The less extreme the topology, the more representative each data point is. To illustrate this, Mt. Washington has the highest average snowfall in the lower 48 (260.6"), but that is because of its location and elevation. That total wouldn't reflect overall state levels since Concordia only averages 63.8". Based on 9 monitoring locations, Michigan averages 80.2". Montana averages 50.4" (6 locations) but is 1.5 times larger, making MI seem like more. But, upstate MI biases the average strongly while the southern half averages are much lower (41.1" Detroit). Since the range for MT is smaller, I would go with MT for snow tonnage. I think a close second is WY, with an average of 76.3" (ranging from 55.6 to 100.4") and 66% the size of MT.
Because of Lake Michigan, MI has more snow than CO (on-going source of moisture versus arid Rockies). Average fall for CO is 39.9" for 4 locations. But CO probably has the most persistent snow.
Or, rather than an overall annual average, how about most days when it snows? Or the snowiest month? In March, Blue Canyon CA receives an average of 50.4" compared to Mt Washington's snowiest month of 43.6". There are a lot of ways to slice it.