Alex, I suppose that approach would work OK in certain circumstances. In others, not so much.

However, your approach sounds like a lot of work, even with an axe. Probably OK if you have a bunch of folks to share the work, and plan to spend several nights in one spot. Since you apparently had tarps, I would just rig a shelter with those. Even without sleeping pads, you can make a pine bough bed. My experience is that properly done, a pine bough bed can be quite comfortable. I would never put a sleeping bag directly on the snow.

An "open air camp in the woods" might be OK in an area with really really stable weather. In my part of the world it would not be such a good idea. Weather can change very fast around here. Going from clear cold weather at dusk to a dump of snow by morning would not be unusual. Going overnight from clear and cold, to rain would not be unheard of. And if it comes to a real blow, you will want a lot more than "wind deflecting tarps".

An "open air camp in the woods" in Alaska would not be what I would call "sustainable survival". In any case, the discussion is about a BOB, which almost by definition is to be ready to grab for a quick get away (not what you dismiss as "pleasure hiking"). The idea of a BOB is fast and light. Cutting down trees every night to build a bed is not my idea of moving fast. The Fiskars Axe you mention looks like a nice product for some situations. I have (and use) a small wood handled axe that looks to be very similar. I like it a lot for some things. However, for a BOB, a small tent, or tarp shelter would be roughly the same weight. It goes up lightning fast, and comes down fast too. And gives vastly better protection from wind.