The best approach for seriously cold weather is still a pair of shooting gloves under a pair of mittens. Like the outer coat, the mittens are removed before shooting. The typical baseball cap is a lousy insulator. Winter is definitely the time for ear muffs in stead of ear plugs. Put a Thermos of hot something or other in with your shells, chokes, wrenches, extra glasses and tickets to Florida.
Cold weather works against the shooter in many ways.
One is that it hardens the targets and makes them physically harder to break. Consider going up one size in pellet diameter. Not a bad idea at all. Also, cold weather lowers shell velocity with some brands of shells and it can make gas guns cranky. Using a shell with higher velocity will provide the extra oomph to keep the speed up and cycle that gas pipe.