Couple of thoughts. First, I've pitched my tent above treeline in the Whites in winter on several occasions, and on two occasions it has been sufficiently miserable that I won't do it again, barring special circumstances. I'd rather lose 1k' elevation and sleep comfortably than save the hour of walking just to not sleep all night. Most recently, we broke trail through extremely deep snow from Appalachia all the way to Madison hut. Having fought that hard to get to that point, we didn't want to lose any elevation and chose to dig out platforms in some deep drifts and pitch there. Wind was steady when we pitched, but it picked up considerably after dark such that my tent was getting blasted all night, and I was pretty nervous. Four-season Nemo - I was pretty sure the tent could handle it. Pretty sure. Further, even though the vestibule was on the leeward side and we were dug in at least 4 or 5 feet down, the spin drift coming up the valley was so heavy that it was constantly blowing under the vestibule flaps or in through the vent we had in the vestibule while we cooked. It was a huge hassle. We could have sealed the vestibule off tighter but chose not to for (I think) obvious reasons. After breaking trail all day we were exhausted, but we still had to fight just to make dinner. And then with the wind blasting us all night and the associated noise and anxiety, we slept little that night and were mentally and physically exhausted the next day. Had we dropped the 1k' to Valley Way tent site, in spite of losing some elevation, we'd have slept comfortably and felt rested for day two.
I find that I'm rarely in the mood to screw around above treeline in winter. I want to do everything as efficiently and quickly as humanly possible, right until I'm snuggled into my sleeping bag in a sheltered spot with hot water bottle between my legs. The prospect of digging and moving snow for, what, an hour or two at the end of a long day while daylight is fading and I'm probably low on calories and getting blasted by the wind is utterly unappealing. I think HAVING a snow cave above treeline - provided you've got a fantastic escape route direct from your cave - would be great. Building one, not so much.
My experience is there are no shortcuts to staying safe in the Presidentials. It's just hard work. I think in net, the quinzee/snow cave adds more work than it saves. That said, I've pitched several times in Sphinx col, and that spot is uniquely suited, I think, to building a snow cave. It drifts in heavy there, and you could probably just dig into a drift without having to pile up any additional snow. But I would NOT head up to that spot without a tent as backup. It's a pretty committed location. A bail out through the Great Golf would be epic, so you're committing to coming back over the ridge at some point. I think you'd want a tent as backup in case snow conditions aren't right or you're just too gassed to dig for another hour.