I bought these snow boots for both my children because in really cold weather, their feet get ever so cold in normal shoes or wellies.
These are so much warmer because they're insulated, and they're fairly waterproof too. I say fairly waterproof because it's only the rubbery part that covers the foot that's waterproof, the top part would probably let in water if submerged. Not a problem if they don't want to wade in deep puddles.
Size wise, I would say they come up large if anything.