I wouldn't put them in something that heavy. Since my kids are still little, I get to decide what they wear, but as they get older, they get to suffer the consequences of their choices (within reason, of course).
As for myself - except for several times when I had to wear a jacket for social reasons, I generally only wore a flannel shirt over a T-shirt for my outdoor attire all winter. When it was snowing heavily, and I was using the snowblower, I would wear a hoodie, hat and gloves.
But then again, I am known for taking off my socks and walking barefoot (in the snow) out to get the mail, rather than go through the effort to find and put on my shoes.