Almost for sure, low top supercell convective snow squalls due occur in Michigan and other great lake states.
There is no doubt that the proper ingredients such as moisture, shear and CAPE would be in place during the cold season near the lakes. The lakes can generate tremedous CAPE from heat/moisture coming off the lakes and very steep lapse rates. (Just take a look at BUFKIT soundings during the late Fall. 1500-2000 lake induced CAPE values happen) Proper shear is more difficult to obtain because it would tend to spread available moisture out too much and weaken convection. Also adequate shear would generally cause lake induced convection to quickly move away from its source of heat/moisture so persistence requiements of a supercell wouldn't be met.
I can think of at least one situation where something like this would mostly likely occur.
Consider Lake Superior and the North shore of the Upper Pennisula which runs basically in a West to East Fashion. NW winds coming off Lake Superior..supply a continous supply of the required heat and moisture...and a West to East boundary that exists inland from the Lake caused either by a lake breeze or some other type of localized convergence..could create a persistent low topped supercell moving along the boundary.
Is there an example of this? Per "Michigan Weather" by Richard A. Keen...in 1987. "A lake-effect "snowburst" dumps 27.5" of snow on Munising on April 1-2, burying cars in 6-foot drifts. Less than 40 miles away at Grand Marais, only 1" of snow falls. As the storm gears up on the afternoon of the 1st, a brief tornado drops out of a snow squall and damages a mobile home on the south shore of Whitefish Bay".
Couple of things to note about this. The tornado is at least suggestive of a supercell. I don't think that this tornado would have been of the waterspout variety as Whitefish Bay would have likely still been completely froze over on April 1 and the South shore is at least 25 miles from Lake Superior. Munising and Grand Marias are in a line West of Whitefish Bay. Another likely necessary ingredient..no snow on the ground. Afternoon heating on bare ground would definately help the cause for more scattered/intense convection.