OM is right on about Georgia. There's "Georgia On My Mind" then there's "Back in the USSR" Georgia.

And here is Mt. Layla-
Mt. Layla

For Mt. Layla, I'd look at a Hilleberg or other quality winter tent. In general, not cheap, though.

Where would you be buying? If in the EU, I would look at Terra Nova, made in the UK
Terra Nova

North Face VE25- a great tent, a bit heavy, but pretty much the gold standard for mountaineering-
VE25

Bask - never seen one in person, made in Russia, so might be cheaper than others-
Bask

A good US brand tent is the Mountain Hardwear line of Trango tents. I have a different brand, but similar design to the Trango 2. Very sturdy design-
Mountain Hardwear

The Big Agnes is not a winter tent. Not what I would want on Mt. Layla judging from the video.

If you look to the left of the page, you will see categories of gear. Look for Winter Camping, then click on Shelter. There is a list of tent makers, including Hilleberg. A good place to start comparing features and prices (in US dollars in the US)