Not too likely, but possible. My buddy's Browning BLR .30-06 froze up (couldn't move the bolt) once while elk hunting in single digits above 0 F. We figured out he had too much WD 40 on and in the action. Took it inside and cleaned the bolt and action and it worked fine. DON'T USE WD 40! I use Rem Lube and only a very light film on contact parts. Your better off running a rifle action dry in extremely cold weather. Off topic, but wanted to share an avoidable operator error that could cost someone a shot at game.
Former hunting partner had his 270 fail to go bang on a pretty nice bull elk in -22° temps at 10k' just north of Gunnison, CO one year. Firing pin locked up in coagulated gun oil; and not that much of it. But at -22°, it doesn't take much.It really doesn't matter what you use to lube the bolt or mechanism up. If you use too much and it is cold you just may have a problem. Even bolt action rifles will have their firing pins be restrictive enough with enough oil on them that the cartridge won't fire when the trigger is pulled. It is best in cold climates to wipe everything down with a dry cloth. There will be enough lubrication left on the parts that you won't have to worry about wear.
But getting that coating of oil off is the main thing no matter what kind of oil you use.
Considering the number of rounds fired on a typical big game hunt, there is zero wear caused by making sure there is no oil, grease, or any other lube left in the bolt/action of a rifle. In hot, dusty conditions, or cold. I make sure mine are devoid of any sort of lube when hunting. Clean, but lube free.