In your case, my vote is the battery, too. They do have an operating temperature requirement and if too cold, then just needs to be warmed up. Even removing the batter and warming it up between your hands is what I've done if you need it quick.
If left too long and it's too cold, if a remote contains "stored values", then they can get reset (cleared) if the "programmed part (aka Flash, EEProm, EAPROM, etc.)" loses its memory and therefore its settings. Like PatnRich mentions, reprogramming might be needed to regain its settings even after getting the battery working again. This is mostly for remotes that can contain settings other that what's the default, but it's something to remember (that's happened to me, too).
I really admire you folks who know how to live in the cold! I am only good at visiting the cold, then I gotta go back south. I guess South Carolina ain't south enough....