I participated in numerous winter warfare training exercises and deployments with 10th Special Forces, the one Group that is focused on cold weather and high altitude training because of our area of operations. My first Winter Warfare was an eye opening experience.
Forget about an igloo. Takes too long and you probably can’t make it anyway if you’ve never done it before.
Forget about the tent. Dig a snow trench. Just big enough for you to put your sleeping pad down. Cover it with a poncho. You will be warmer than in a tent. Snow is an insulator but you don’t want to get wet. You can glaze the walls of the snow trench with a candle to keep them from crumbling if the snow won’t hold.
It is key to stay off the ground/snow below you. The cover keeps the warmth in. I woke up one morning to find the poncho just about on top of me, but nice and toasty since six inches of snow had fallen overnight, adding to the insulation.
What a tent will is block the wind. But usually you have a lot of space that will dissipate your heat.
I was also known for not carrying a sleeping bag. I carried extra thermal middle garments and would put them on, then get inside a Goretex bivy sack at night. It also helped when I had to pull security at oh-dark-thirty.
Another lesson learned was to not bring weapons into the snow trench. They’d sweat and then freeze. We left them outside on a rack made of branches or ski poles.
One of the most important things in cold weather is to stay dry! I used to give time warning for the team to strip down before moved out, usually to just our polyprop undershirts, putting the rest in our ruck. We were freezing when we started but warmed up fast with over 100 pounds of gear plus weapons, etc, cross-country skiing.