To help put cold temperaturee accuracy in perespecive, consider the following. When Anschutz tests their biathlon barreled actions from a vise/fixture in test tunnels in cold temperatures, the accuracy standard is ten shots within 17mm outside-to-outside (some reports have it at 18mm). That's center-to-center ten shot group of about .450". By comparison, when shooters lot test for ammo in "normal" temperatures, ten shot groups above 15mm OTO are considered unacceptable.
There are three major factors with regard to .22LR accuracy in cold temperatures.
First and probably most important is the ammo itself. Typically, colder ammo will have slower muzzle velocities. As temperatures rise, MVs increase. Temperature differences between individual rounds can affect performance. Biathlon-specific ammo is distinguished by having higher MVs than other match ammo.
In cold temperatures, when keeping ammo warm by various means, it's challenging to keep all at or near the same temperature when it is actually shot. Biathlon shooters don't warm the ammo and keep it as constant as possible by not warming the magazines.
Bullet lubricant is part of the ammo factor. Many top biathlon ammos have lubricants designed to be effective in colder temps. Some ammo sold as "biathlon" ammo, SK varieties for example, will have the same lube as other ammo. When it's cold, the bore may not become consistently and evenly lubricated. This will affect accuracy performance.
A second factor is the rifle itself. As alluded to by Jerry, when it's very cold, firing pins and rifle lube may not function as consistently as in more usual temperatures. The barrel itself will not warm very much from shooting but it's not clear if in the cold the barrel itself will perform differently. What's more significant is that in a cold bore lubrication doesn't perform as well as when it's warmer, regardless of the ammo used.
Finally, as others have noted, it's much more difficult to shoot consistently and well when it's cold. Accuracy and consistency don't improve as temperatures drop.