I grew up in a suburb of Buffalo, NY in a snow belt.
Sometimes we had more snow and were colder than Fairbanks Alaska.
I survived the Blizzard of 77 (22 ft drifts).
I think you need to consider what you want out of winter.
There's Winter! - Fluffy snow flakes, hot chocolate, frost, icicles, skating, snowing, sledding, snow angels, snow forts, snow men, occasional snow days off of school!
And then there's WINTER - 6 or more months of cold and shoveling, -20 degree wind chill factors, engine block warmers, car cancer (salt/chemicals used on roadways can REALLY eat the metal on your cars), learning to drive on snow and ice with zero traction can be fun(not), ice dams forming around your gutters (roof damage), clomping around in boots, and lugging around winter jackets.
Lake effect snow and total white outs (zero visibility as in you can stick your hand out away from you and you can NOT see your hand on the end of your arm) can be alarming.
Winter can be exhilarating but growing up in the thick of it meant:
You get up and before you leave for school you shovel the driveway.
When you come home from school you shovel the driveway again.
And before bedtime, you shovel the driveway one more time so it's not so deep in the morning.
And at anytime a snow plow can come by down the road and dump a 2 ft drift of rock hard snow and ice at the foot of your driveway and you get the 'pleasure' of chiseling it out - AGAIN.
It's exhausting.
Pick someplace that gets some snow - but not all the time, or it snows and melts away fairly quickly.
Anywhere in middle of the country and you will be subject to periodic Saskatchewan Screamers and/or Manitoba Manglers (severe bone cold arctic cold fronts).
You might like Albany, NY - they get some cold and some snow but they are not consistently hip deep in it all the time.
I have no desire to live in snow anymore.
Where we are now, it'll snow maybe once or twice a year and that's enough for me.