Winters are very up and down, mostly up, but there can be some definite downs, too.
Often it's very pleasant and in the 50s and sunny.
Often it's very dreary and in the low 40s and raining.
Often it's below freezing at night and in the morning when you get up to go to school.
Sometimes it's very cold (overnight lows in the teens, occasionally in the single digits).
Occasionally we get significant snowfall (as in it sticks and they close school — no snow removal equipment here so we just wait a day or so for it to melt). Your kids will want to play in it then and I do think keeping some snow pants if you already have them is worthwhile for these occasions. It's just miserable to try to play in the snow in jeans and have them get all soaked. We probably average one snowfall a year where they have to close school. That means some years there aren't any snow days and some years we get more than one significant snowfall. I wouldn't go out and buy snow pants new, but I do keep some around that I have picked up at the thrift store. It's nice to have some waterproof snow boots for the same reason, but again we may have a winter where you don't need that stuff.
You do need a warm coat, especially for those early mornings getting ready for school.