What happens to air when it gets extremely cold?

Air does not get more 'dense' or anything similar to that, but it does lose temperature and thus house snow if it rains!

Well, pressure is inversely proportional to volume

and volume is directly affected by temperature

so I imagine it does, yes.

Yes it does.

But, because air isn't a pure substance, rather a gas blend, it liquifies in a sorting by flavor process.

The first gas to condense out of air is water vapor.  This is familiar to you everytime you see a film of droplets on your cold drink containers, or everytime you see water pour out of the air conditioner.

Next gas to remove is usually Carbon dioxide.  It doesn't condense though, it rather deposes.  Carbon dioxide doesn't form liquid unless it is subject to about 6 atmospheres of pressure.  Carbon dioxide deposes to solid dry ice if cooled out of air.  If dry ice is subjected to heating, it will sublime back to carbon dioxide.

Following that are the main constituents of air, namely Oxygen and Nitrogen.  I believe that Oxygen condenses first, but I'm not really sure.  Please correct me on this.  Next flavor to condense, just slightly colder, is the Nitrogen.

This is indeed how they enrich air, to get pure oxygen, or to get pure nitrogen.  Or to select to buffer oxygen with a different flavor of gas, like helium, which is what we do in filling SCUBA tanks.

Following that, the minor noble gas constituents will condense out of air.  Most of it is Argon.



FYI though, gas mixtures work particularly interesting, in that rather than a constant temperature phase change like what happens in pure substances, temperature continues decreasing as each flavor condenses out.