Why are eggs not stored in the fridge better in baking?
This isn't at all exclusive to eggs, searing off a really cold (fresh, not frozen) steak will get you a tough steak. Unless the recipe depends on the behavior of a protein as refrigerated, proteins are better to work with at room temperature.

Think of the egg yolk and white sort of like ice cream; the warmer it becomes, the more distinctly the viscosity changes. Beating cold egg whites to stiff peaks is one heck of a workout :) Cold yolks are also very likely to result in 'broken' emulsions. 

In your specific case, cold eggs simply won't incorporate into the mix in a manner that's consistent with what the recipe previously produced. The difference would depend on the recipe, but in most cases, not subtle. Things would be denser than ideal, or just simply not hold together very well. It really depends on what you're doing.