I think, the picture was taken from the flatter end of the den. It is customary to build those things by digging at an angle approx. 45°. As far as I came to know, that's because of statics and wind shelter. Also the opening should be the side opposite the wind.
Taking that into account, it was less snow than it seems they had to move.
As it happens: We do have snow at the moment, which seems to get a more and more rare occasion. Not as much as in Siberia, that is, but enough for my nephew to venture on an endeavor of his own. He build a hill from snow and dug a hole in it from left to right. Or front to back, or wherever you might be positioned. ;)
He took some days for it, but I doubt his parents let him work on it for more than an hour at a time. Then again he was pretty alone working on it and he's just 7 years old.
On the other hand it's known that soldiers build those kinds of shelters when in snowy areas without tents and such. But I daresay they'd have some kinds of tools with them.
I think, the probability of the hikers building the den by themselves depends highly on the timeline you base your theory on. If it's a matter of just one, maybe two hours (as Rakitin does) it's highly improbable. If they took more time, they might have done it. Also working on the den would have kept them warm and at least at later stages out of the wind.
I'm not sure, ash, how much a puttee would help you building a den. It might keep your hands a little warmer, but that's about all. Rakitin reported another puttee to have been found in or near the tent (can't remember), that was brought to Ivdel. But because Juri Judin couldn't say to whom it belonged, it somehow disappeared. Couldn't verify that as of now.
But I've been wondering, if these two belonged together and maybe did belong to Zolotaryov. He was ex-military and Juri didn't know his clothes as well, I'd say...
I'd agree with Monty on the part, that the shelter was surely much flatter when it was build and snow accumulated on it over time.