One of the top survival priorities for doomsday preppers is shelter. And as preppers we should be planning for the worst; which would mean having to backpack out from a region of disaster carrying all our survival gear with us. So the first order of business to provide for your bug out shelter is a great sleeping bag, and a lightweight, backpacking tent or bivouac.
We also can’t predict in which form doomsday will decide to present itself, but many doomsday scenarios result in extreme cold weather events. An asteroid or comet strike, a major volcanic eruption, a gamma-ray burst, or nuclear war could all result in drastic temperature drops. For example around 530 AD the world experienced an extreme cold weather event in which it snowed during the summer. 1816 also experienced summer snow, and was likely caused by an Indonesian volcano. The point here is to plan for the possibility that you could be bugging out on foot, and in very cold weather; so your bug out gear should include lightweight tents and sleeping bags designed for extremely cold conditions. And if this extreme cold weather doesn’t occur, you can always adjust and remove layers.
The most important part of your extreme cold weather bug out shelter is going to be your sleeping bag. But to protect it from water and block wind you’ll need a waterproof, backpacking tent or bivouac sack. If you will be bugging out with a family, the most efficient option will likely be a tent (or multiple tents). There are 2 or 3 person tents which don’t weight much more than single person tents, and don’t take up much more space either. On the other hand if you expect to be bugging alone, consider a lightweight single-person bivouac sack to save a bit of carrying weight.