Here is the clothing and shelter from a ski trip last weekend with my 5 yr old.
Temps were highs in mid 20's(-5C) and lows around 8F(-13C).
For clothes she wore:
Smartwool Kids Ski socks
Midweight HH long underpants
Icebreaker longsleeve lightweight merino shirt
Cioch Kids pants and jacket: These are made from Nikwax Analogy, the same fabric as Paramo.
While getting ready at the car, we put our down jackets over the top, and she never took hers off again.
Marmot Kids Amadablam Down Parka
Then in camp I added:
Fleece pants (under her shell pants)
Exchanged ski boots for snow boots(Keen)
Thin fleece gloves
At night, she removed the Cioch suit and down jacket and put on:
Dry socks (same as others)
My wife's Goosefeet down socks.
She slept in a regular size Marmot Col Dryloft, -20F (-29C) down bag, with a Gore Dryloft shell.
She started out on an old style Neoair on top of a 1/2"(12mm) closed cell foam pad, but ended up on just the foam pad, because the airmat was sliding around to much.
Next time I will just bring one pad for her, little kids just can't deal with stuff moving around at night.
We slept in a Hex3, a floorless tipi tent. This was alright with the cold, dry snow and consistently freezing temps we had. If it was any warmer I would bring the inner tent, as it is hard for me, let alone a small child, to keep snow off your sleeping pad and stay on the pad at night.
The floorless tent did have the benefit of being able to let her take a pee break without getting out of the tent, making that much quicker and easier.