Not with the ventilation above their heads.
We keep the chickens dry -- which requires generous ventilation at the top of the coop -- they keep themselves warm with their built-in down parkas. They're fine down to at least 0F and even below as long as they're dry and out of the wind.
This...
If you prop it up like that permanently, fill in the gaps with hardware cloth, and make top-hinged vent covers to keep the weather out that will give you the ventilation you need. :)
Yes, people do that -- usually as a run rather than a coop though.
Hardware cloth is better than chicken wire because dogs and raccoons can rip right through chicken wire.
Draft-free doesn't mean no air movement at all. It means that there's no breeze strong enough to ruffle the birds' feathers when they're sitting on the roost.
Look at my brooder, where I raise chicks -- it's 4x8 with 16 square feet of permanent ventilation and another 10 square feet of...
First thing,
Is that a top-hinged vent across the front of the coop in the first picture?
If yes, open it up and leave it open. It may not be enough ventilation, but it's in the optimum position at the top of the coop.
You want at least 1 square foot of 24/7/365 ventilation PER BIRD (I...
Here are some hoop coop designs.
Yes, they can take snow load.
https://www.backyardchickens.com/articles/hoop-tractor.69336/
https://www.backyardchickens.com/articles/hoop-coop-brooder-with-roll-up-sides.75720/...
Oh dear. You seem to be in quite a predicament.
Where, in general, are you located? Climate matters a lot because "Snow and freezing" varies from inches with temps measured in double-digit positive degrees farenheight to measured in feet with temps measured in double-digit negative degrees...