Just take the gun apart completely and dejunk everything. You had some kind of gummed up lube in there that slowed the firing pin in the cold weather. Don't put it back together with enough lube to attract dirt or gum up.
Be sure you know how before trying to take an Ithaca apart. For one thing, remove the stock before cranking on the receiver screws. They hold the hanger that the stock draw bolt screws into. Without removing the stock, those screws are under a lot of tension and could be damaged with too much screw driver force. Get a schematic.
DF
