Posted this in off piste too, as probably fits better there, sorry for the duplication.
Bit of background, I've spent a fair bit of time in Kyrgyzstan, but usually in the summers. If you are looking for a place to visit a bit off the beaten path, with excellent outdoor activities, and an interesting culture I can highly recommend it. This overview will focus on my recent ski touring trip focused around Jyrgalan village.
Jyrgalan is a little village at the foot of the tian Shan mountain range, in the far East of Kyrgyzstan. Once famous for its coal mine, but after the fall of the Soviet Union the economy collapsed and most people had to move away. You can still see the old mine, and some of the bigger now abandoned buildings. Due to its location it's having a resurgence as a hotspot for tourism (hiking in the summers and ski touring in the winters).
To get there you will need to fly into Bishkek (capital of Kyrgyzstan). From there you can organise a transfer to Jyrgalan (arrange this through destination - see above for contact info) or you can go via public transport - taxi to Bishkek bus station, bus to karakol, then bus to Jyrgalan - total cost around $10-15. Expect to take around 8 hours driving in total.
If you want to break up the journey karakol is a natural place to stop. There is a decent ski resort there, that's nice for a warm up day and a few other sights, cafes, restaurants, Lenin statue etc. Also if you need anything (supplies, clothing, toiletries etc.) best to pick them up here as there is very limited availability in Jyrgalan. Saying that, there is actually some decent touring kit available to rent in Jyrgalan, including avalanche backpacks - best to reserve in advance through destination Jyrgalan (the local tourism board - https://jyrgalan.com/ email: destination.jyrgalan@gmail.com) as limited supply.
For accommodation in Jyrgalan I can recommend Ala Kol guesthouse. Good food, can also provide packed lunches, modern rooms, WiFi, friendly hosts etc. Also have a nice banya (russian sauna) that's well worth trying out after a long day ski touring. You can see prices and make reservations through the booking.com website.
There is a cat ski operation (https://rycetravel.com/en/tours/cat-ski-kyrgyzstan/). I didn't personally use them, but looked pretty professional. They seemed to be taking a group up every 2-3 days, so there is definitely a possibility of joining a group if you don't have the numbers to fill it yourself. They only operate to the south west of the village, so even if that area gets a little tracked (relative to the area, it's certainly not Whistler!) there's still plenty of other options for first tracks. On the positive side for ski tourers the cat makes an excellent access track for easy skinning, and it's possible to branch off it to many areas the cat can't reach. There is also options for uplift via skidoo and in traditional Kyrgyz style by horse (contact destination Jyrgalan to arrange this).
In terms of terrain there is a nice range from mellow meadow skipping to serious ski mountaineering stuff. All of it can be accessed directly from the village, which is nice. If you are looking for some first descents it's a great choice as not a whole lot of skiing has been done here yet. I've uploaded some photos to try and give an idea of some of the local terrain, the photos are by no means extensive lots of areas and lines not covered, but hopefully gives a general idea https://photos.app.goo.gl/gyqekbUeEULic2ea8 . When I get around to it I will try adding some routes I did to fatmap. For some more views of the terrain and a little video inspiration from Aurelien Ducroz (from chamlines) http://youtube.com/v/K7v1w4loLjs
If you want to make a bigger trip of it there are more ski opportunities in the area and around the country, as well as a pretty modern resort just across the border in Kazakhstan (shymbulak resort). If you want to experience some non-ski more cultural stuff you can go and meet the eagle hunters (they use golden eagles to help them hunt, not actually hunting eagles!) which can be combined with visited fairytale canyon for a pretty cool day out.
Definitely interested in going back in future, so if anyone is keen let me know and perhaps we can put together a group. Also feel free to ask any questions and I'll do my best to answer.