I carry a very lightweight folding saw (for winter ski/snowshoe dayhikes only), something like three lightweight (not the thick contractor type) yard waste bags, the lightest metal-head shovel I could find, and a length of candle. Optionally, depending on the trip, I might carry one of those plastic disc units made for emergency digging in snow rather than an actual shovel.
If snow is deep enough, my go-to survival shelter is a trench. Snow caves take too long too dig and too much energy, and you get too wet typically doing it, plus they require a certain degree of expertise and experience. So IMO not a good choice for an emergency situation. I've also heard of shelters built by reinforcing tree wells. Fine for blocking wind, but you need to create a warmer environment IMO.
Trench deep enough optionally to be able to sit up in the trench (or not, depending). Cut live branches (LNT goes out the window if my life is truly in danger). Line the bottom of the trench with live branches, and cover the top of the trench with longer/stronger branches plus trekking poles. Cover that with split-open yard waste bags, cover those with some inches of snow. Put on all your clothes, crawl in, cover opening as best you can, leaving enough ventilation for safety. Light candle.
In situations where there's not enough snow to trench, build a debris hut instead, similarly using all of the same tools, cover with plastic, cover result with snow.
It's always a compromise between safety and weight carried in terms of winter emergency gear; certainly some warm puffy clothing is very important too. But the minimal for me is these few 'tools' plus the knowledge of how to use them to build a fairly simple and easy shelter.