Good points all. I started "tarp" camping in Scouts and continued post-Scouts because 1. Cheap, cheap, cheap and 2. versatile in the PNW Cascades, where there are trees aplenty for stringing them up myriad ways with ridgelines sufficiently strong to shrug off nearly any weather. Note: I never intentionally headed into the snow with just tarp makin's, but snow sometimes found us. YMMV

Tarp back then: a hunk of Visqueen off a very large roll.
Tarp today: either a flat or catenary-cut lightweight fabric sheet with plenty of tieout anchors.

Pyramid or teepee shelters aren't tarps in my book, but I can imagine how they might acquire the moniker anyway. Floorless shelters works for me, although it's a rather broader category than just teepees.

As to our new friend Becky's question, I'd ask for further input. Do you want a snug, well-protected space for sleeping or do you want roomier longer-term living quarters that, among other functions, allow you to cook inside or in a vestibule and accommodate all your gear?

There are many lightweight tents for sleeping, rather fewer for hanging out during a multiday blow. Then, there are construction decisions. Single-wall, double-wall, tunnel, wedge, dome, self-supporting...?

The "best" extreme shelter I've used was an Early Winters Omnipotent with vestibule; the best I've owned is an EW Winterlite Goretex. Both are/were tunnel-style, requiring anchors fore and aft. Both are fast to set up and handle very high winds and reasonable snow loads, although I think in general, tunnel-style tents can require more frequent digging out than some other designs. The O-tent was double-wall, with the inner tent suspended at each hoop pole.

My qualms about double-wall tents with non-attached flys revolve around the more complex, time-consuming setup and the need for lots of anchors to keep everything taut, as well as the tendency for the fly to gather snow and press against the inner tent. Some designs seem to fend these tendencies off, but I don't have the hands-on experience for a recommendation.

If such a thing were available, I'd buy an updated version of my old Goretex tent done in eVent with carbon fiber poles. I'd be happy to take such a shelter almost anywhere, or at least anywhere I'm ambitious enough to go these days. Based on what I see on the market today, I'd probably buy a WPB wedge and learn to anchor it properly. If I were going to hang out in the snow over an extended period, I'd consider a Kifaru rig.

Cheers,