Just clean as normally, the above suggestions will work well. Modern lubricants generally function well in the cold, better than the "operator".

If you handload for such conditions, Magnum primers may ensure more consistant ignition in cold temperatures. Also, loads developed and tested in cold weather, might be a bit on the "hot" side in Summer type temperatures. Powders vary considerably in this respect.

In very cold conditions, the "heat waves" off of the barrel can be spectacular!