some of the heaviest snowfalls to Michigan's upper penninsula. I believe there was some 39 feet at Ontonagon in 1936
That doesn't see so odd to me (except maybe for a two-year lag).
One doesn't need particularly colder temperatures to get snowfall. With the greater warmth would've been an stronger, on-going engine to keep more moisture as uncondensed in the atmosphere. When that extra moisture finds cooling to condense it out, along with some residual lifting to allow for a maturing winter thunderstorm, down it can come, with an apparent vengeance!
HF
There is a demonstrable cycle of weather in the Midwest. Before the Dust Bowl, there were the Panics of 1873 and '93 -- when droughts ruined farmers and crops west of the 20" rainfall line. Then, another brief drought in 1907.
Following the Dust Bowl, there was an extended drought in the early fifties and another in the late-nineties.
You'll note a pattern -- about every twenty years, it gets unusually hot and dry in the Midwest. The only exception was the 1970's -- when the normal drought pattern didn't repeat. And that was when the climate alarmists started bleating about a New Ice Age.
Note: Facts reported without benefit of a computer model...