It used to be that firearm maintenance was more tedious and certainly more frequently needed than it is currently. This is the result of modern engineering and chemistry, which has given us stainless-steel barrels, actions and anti-rust metal coatings such as Cerakote. Synthetic and laminated stocks are tough and easy to maintain. Current barrel solvents dissolve copper and lead from bullets, preventing pitting and lead/copper residue that leads to inaccuracy and shorter barrel life. Of course, the science behind modern powders and bullets generally results in extreme accuracy and reduces wear on the bore.
It wasn’t long ago that the rule was to clean your gun after every time it was used. This is still a good plan to follow but not as essential. Obviously if the firearm got wet, it needs to get some TLC, as rust or other corrosion can still occur. The treatment is pretty simple: just let the gun dry and then wipe it down with a treated (oily) rag and bore cleaning rod. Surprisingly, light surface rust can be readily removed with (of all things) oil on a small piece of wool felt, as found in winter boot liners. It is just abrasive enough to do the job and won’t remove the finish on the metal.
Winter hunts, except for ptarmigan, are limited to caribou (in a few locations), and bison. During these hunts, a few steps or precautions can keep firearms problems to a minimum. One of the more easily solved difficulties is the rifle freezing to the point that the action cannot be opened to load or unload. A similar situation can result, with the freezing of the firing pin mechanism, to where it doesn’t release at all; or a worse situation where the freezing causes the delayed release of the mechanism (a hang fire). These can be minimized by removing any oil (lubricant/rust prevention) by cleaning the action with a solvent to remove the oil. Other than oil, moisture also can cause major challenges to be avoided because when it freezes, similar to lubricating oil, it locks the moving parts of the firearm so that nothing moves. Moisture can and should be avoided and it is simple to do so. Unless the firearm has been dropped in the snow or into water, moisture is immediately created when you bring a very cold firearm into a warm environment such as a tent, cabin or vehicle. The moisture appears everywhere including inside the stock where the action and barrel are seated.
A straightforward way to prevent this from happening is to just not bring the gun from a cold environment into a warm one. You can put the gun in a closed case and let it warm up gradually inside the case or just leave the gun in the cold environment outside the warm area. You can put it in an unheated vehicle or locked in a gun case on an ATV or snow machine. Binoculars, cameras and other optics can be treated the same way to keep them working. They all need to be warmed up gradually.
Tape over the muzzle keeps snow and mud out. Carry a cleaning rod to remove an obstruction in the barrel.
My Canadian Tire metal gun box sits on short pieces of two-by-fours, to keep it off the cool concrete floor in the basement.