Frozen beer is not an issue. No need to worry about that.
So to review: your primary fermentation was some where around 50F-60F? Once primary fermentation was finished (Hydrometer reading?) you put it outside to lager at almost freezing temperatures? When the lagering stage starts the fermentation is supposed to be finished. Lagering's primary purpose is to allow the yeast to settle out and take as much of the tannins and other substances with it. This is what gives the clean taste at the end.