If a person is so inclined,search for "Thermal co-efficient of expansion" of whatever material you want.It likely can be found.I seriously doubt dimensional changes are the issue.If the gun locks up,it ice or frozen lube.
I am not a metallurgist or Mechanical Engineer.I do not pretend to know the answer.
I'm pretty sure the stainlesses are more likely loose strength under extreme cold than the carbon alloy steels.
I can offer a little evidence.If you take this link to the Kreiger barrel page,you will be on the "calibers" table.Look down the page to a black header that offers Obermeyer 5R rifling.Right under that is a note explaining why they offer lighter contours in CM steel than 416 stainless,and it has to do with cold weather.
http://www.kriegerbarrels.com/Calibers__Prices-c1246-wp3390.htm
Schuemann is a highly regarded handgun barrelmaker.He uses 416R steel.He is willing to discussconcerns about 416
http://www.schuemann.com/Portals/0/Documentation/Webfile_Barrel Steel.pdf
If you want to learn the horrors of what some solvents do to 416,Mr Scuemann has some to say about that,too.
Especially chlorinated hydrocarbons like carb cleaner.Or,a really good one,the tapping fluids based on chlorinated hydrocarbons.Old formula Rapid Tap,for example
http://www.schuemann.com/Portals/0/Documentation/Webfile_Barrel_Cleaning.pdf
This link is to an Alaskan forum,discussing stainless vs CCM steel in cold
http://forums.outdoorsdirectory.com...-of-stainless-steel-Guns-vs-carbon-steel-guns
It starts out slow,same old opinions,till you get to case study about Ruger and the 454 Casull,how 410 and 416 did not make the cut,Carpenter steel consulted,etc. Ruger went for the good stuff.
I came away with this:"Stainless" covers too many steels.There are a lot beyond 304,410,416,etc.It does not work to characterize them all together.
I have some experience with 17-4 PH.Freedom Arms uses it.MOA Maximum uses it.I have a few treasured chunks.Its a bit tough,machining,but it machines crisp,clean...nice!!
And,bake it a couple hours at 900 f then air cool it,no warp,no scale,and someplace in the 40's Rockwell "C".Very high tensile.
Want to play with thermal coefficient of expansion?Ok,just realize the whole gun is the same temp,so the bolt,bbl,receiver,etc will all change together,although,perhaps at a slightly different rate.Not much.
http://www.engineeringtoolbox.com/linear-thermal-expansion-d_1379.html