I have 5 kids and live in NH. I have a degree in kids' outerwear :-)
For your 6 year old: LLBean kid's cold buster waterproof gloves are amazing. Waterproof, fit well, last forever (or until your child loses one).
For your 4 year old: check out Lbow mittens. They are mittens with a sleeve that goes over the child's coat sleeve. This solves the problem of mittens slipping off when playing in the snow. It also keeps snow out of the wrist area - where the jacket ends and traditional mittens begin.
An added bonus: with LBow mittens you will never hear "Mom, fix my mitten!" "Mom, my mitten came off again!" requiring you to remove your gloves to fix a mitten situation!
Here's the website:
https://www.lbow.com/
T. Y
SAHM of 5
(14, 12, 6, 5 & 2)