Use those socks
This is a great old fashioned way to keep kids warm in deep snow.
The biggest complaint from my boys when they were younger - cold snow on wrists and ankles when they'd be out playing in the snow having a great time. Solved this by using knee socks - with holes cut out for finger area and thumb if they wanted gloves on or just a thumb hole if they were wearing mittens - put on before the jacket and they keep the wrists warmer. For the cold ankles - after the snowsuit is on, slip on a pair of men's winter socks before the boots go on... helps keep the snow from dripping down into the boots.
For infants who lose their mittens - just slip on a pair of chilren's knee socks before the jacket and mittens go on. Their hands will be covered if the mittens slip off.