Contrast the Bud Grant era Vikings of the 'frozen tundra' to the modern Green Bay Packers and their natural grass field. They work very hard to keep it alive during the winter, I'll bet, with the underground heating pipes, etc.
But yes, whenever possible, natural grass is the way to go. The difficulty and cost associated with keeping a natural grass field is undoubtedly why artificial turf is a thing.
Edit: And doesn't Green Bay also have the synthetic webing/plugs weaved into the natural grass, like we now have?