Why do we only get snow after days of hot rain?

It's been a couple years now since we got snow when there's been snow
on the ground.

We always get a nice dump of fresh snow one day after all the previous
snow has been melted by a two-day bout of heat and rain.

What's up there?

Why does there have to be a hiccup of heat/rain before a big snow dump?

--Here in Mid-Michigan, anyway.

Does heat ride ahead of snow in these weather systems?

Why can't we have cold weather, then snow, then cold, then snow? It
that too much to ask?

Maybe it always gets a bit warmer before a snowstorm and it's just that
now with global warming it's warming into the rainy-40's before
snowing. It gets to snowy zero then swings up to 40 and bare ground.
Maybe in decades past it got to 20-below zero then swung up to 20 with
fresh snow.

Is it just that the swings are higher up on the temp-scale?

--JP