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Just like how balls go cold would result them in going less farther, would a freezing cold clubface affect distance in anyway?

In "any way" sure. In any significant way, I would think not. I think that the cold balls things is generally overstated -- the distance loss is a combination of a lot of factors that each individually aren't that large, but the sum of them makes a difference. I personally think that the most significant is the extra layers of clothes and the stiffer muscles from the cold, though the cooler air temperature and balls do add in too.

Well as a private pilot I can tell you cold air is much denser than hot air. In my Cessna on a cold winter day, I can take off at 55 in just a few hundred feet of runway. Hot summer day I hope I don't run out of runway here is TX before I can lift off at 75 to 80, and then hope I gain enough altitude quick enough to clear the trees and high wires.

If anything cold will make the steel harder and denser, therefore help out, but between the cold heavy air, hard ball that you cannot compress as much, extra clothes, and all the other elements will kill your distance in the winter.

You want to hit it far, play a high desert course on a hot summer day.

Or go to Boulder, Colorado, 10% instant distance increase.

Keeping one's golf balls warm in the winter, WILL give you more distance. I've tested it and can see a measureable increase in distance with warm golf balls compared to cold one in the winter. Same clothes being worn, same air temperture, so it has to be the ball temperture, it's the only varible left.

Try Flagstaff or Lake Tahoe area.