Wanna bet? The nearest great lake to me where cold arctic winds come down from the north is Lake winnipeg, which is frozen solid. No "lake effect" occurs after the ice has formed. In the Northern east, yes, but those lakes are below my latitude. I'd only get lake effect from Lake Michigan if there was a strong wind from the east, Strong enough to carry moisture right over Minn. into ND, which is very rare.
That's why I said 'open water'. If you have open water and it is -100, it will snow. So if it is not snowing, it is because the lake is frozen, not because it is too cold.
I am south of Lake Erie. It's now 90% frozen, so my lake effect snow is a goner until late March, early April. We sometime get good amounts then as the lake is opening up again.