With this happening now, I'm curious.
How do you create adventures in such an extremely cold environment.
You either add rules for dealing with extreme cold, or you just describe things differently.
The "just describe it" method is where you focus on how cool and heroic the characters are, rather then spend a lot of time worrying about details. I find this to be the more popular way of playing. Characters might need to purchase cold-weather gear and such, but beyond changing character appearance you don't
have to do more. ()especially if you have magic coats and such)
But a lot of people won't find that satisfactory, especially if your point of reference is Northern Siberia. Then you'll need rules. The DMG has a couple paragraphs, but you might want to find/write some homebrew rules to create interesting choices.
How does an intelligent species (ex garter snake men) survive the worst of this so they can prosper in the spring?
If they're warm-blooded, the same way humans do, mostly. There's a lot to be said about this but peoples like the Sibr and Inuit have lived in environments like this for a long time and have developed a lot of technologies to do so - you can research those an adjust.
Cold-blooded creatures (ie snake people) would have a much harder time and would probably live near major heat sources (volcanoes?), possibly even retreating underground through the worst of winter after storing enough food to survive that long (which, being cold-blooded isn't as much as a warm-blooded creature would need.)
When they do go out, finding ways to keep warm would be the biggest challenge for them.
What sort of encounters would you expect?
Ice monsters, extreme weather (possibly including magical cold), ice-themed undead, extremely hungry snake people wearing a lot of furs.