My "56 Plymouth manual calls for 50 weight for temps above 32 degrees, and 20 weight for temps below that. The 50 weight for warmer temps is much heavier than what should be used in the crankcase which would be 30, 20W-40, or 10W30. The heavier, straight weight grades of oil are available as racing type oils.
I figure the engineers that designed the engine know a lot more than we all do, so I follow their advice.
In choosing oil for an engine that will be kept inside and warm, maybe heavier, warmer temp oil for the engine and lighter, cold temp oil in the air cleaner since it will be sucking in the cold air. I think that is what I would do.