I am sure I bring less then I should, but finding that edge is one of the main points of this site. Now that I may often have one of my kids with me, the issues get even more difficult.
Since this is likely an emergency when something has gone wrong, I am not sure how realistic a snow cave or debris shelter would be. We have lots of trees in Vt, but looking around on the mountains in the snow, there is a lot less obvious cover than one may think, particularly if you had a broken leg or other serious injury. Making a fire may also be challenging.
I pretty much never bring insulated pants or a sleeping bag. I just can't get my head around laying down in a trench in the snow for the night, it seems way too exposed. So for the past few years, I have been bringing my poncho tarp, figuring that would let me rig a shelter, plus maybe a mylar or thermolite bivy sack, plus an insulated jacket. I can never decide on the esbit stove, so that is in or out, and a candle often makes it in.
But all this leads me to say that the bothy bag concept seems like the best and most robust option, better than bivy sack, a tarp, a debris shelter or a snow tench. It can shelter someone injured, multiple people can share, it provides protection from the elements, and would allow a change to regroup and renavigate, and fix gear, like having to fix bindings, etc. So I don't have one, but really am talking myself into making that purchase and giving it a try. I had never seen the link to the ones at Brooks Range before today, so that now gives a real choice vs the terra nova options.