Placing glasses in the freezer is one of those practices that almost certainly began to further cool beer that was borderline cool when poured into a really heavy mug that was warm. Sticking this heavy mug in the freezer not only solved the warming problem, but it actually cooled the beer. Of course if the glass is wet when placed in the freezer, ice forms on the surface of the glass. Ice, when viewed under a microscope, is very jagged and is like thousands of tiny daggers. These small, irregular features act as nucleation sites for carbon dioxide bubbles. This is why carbonated beverages foam when poured over ice with a dry surface.
One geeky trick when pouring soda pop over ice plucked from the freezer is to polish the surface of the ice with water. Simply fill an empty glass with ice, pour water over the ice and pour out the water before pouring in your soda pop, and voila, no foam! Did I mention this is really geeky?
Bars that store beer mugs in those special mug freezers usually pour their beer slowly to deal with foaming caused by the ice layer or they end up pouring foam down the drain and wasting beer during dispense. This is caused by the nucleation sites on the glass surface.
Fast forward to beer drinking. When you take drinks from a beer glass that is topped with foam, the foam adheres to the glass as the glass is emptied. Beer foam dries over time and the protein-rich foam becomes like an egg meringue hanging to the surface. This dried beer foam is much more coarse than ice.
In your case you are coating the surfaces of your mug with dried beer foam, that is if you drink slow enough for the foam to dry, and you are probably leaving a little residual beer in the bottom of your glass before you stick the whole thing back in the freezer for another cooling off period. When you pour your second beer in this glass there are more nucleation sites and your second beer foams more. More foam means more dried beer foam adhering to the glass at the end of your second beer. You now repeat this cycle once again, only your third beer is being poured into a glass absolutely teaming with nucleation sites … poor beer!
I am not a big fan of frozen mugs for a few reasons. One is that super cold beer has suppressed beer aroma and flavor. I prefer pouring flavorful beer into a clean, room temperature glass with a wet surface. The wet surface is like the ice polishing trick and you get a smoother pour with a wet glass as compared to a dry glass. Another reason to steer clear of frozen mugs in bars is that the liquid frozen in the mug is often the cleaning water from a triple sink. Most states require the third sink to be filled with a sanitizer solution, usually dilute bleach or quats. This means the frozen liquid in the beer glass is something that you really would rather not mix with your fine beer, let alone actually drink. This is the same reason that stacked glasses are kind of gross … the liquid from the third sink does not drain from the glass and is trapped in the stack of glasses. This ensures a tasty shot of sanitizer with every pour. And the third, as if another reason is really required, is that frozen mugs cause beer foaming.
If you don’t want to wash your beer glass between uses, I suggest thoroughly rinsing with water to remove dried foam. And if you like keeping your glass cold, try filling it with cold water from the refrigerator to chill after rinsing.
So you are concerned that pouring beer through a draft line may have the same sort of effect of building up nucleation sites on the wall of the beer line as using the same mug a few times between cleanings. This is really not much of a concern in my book if the beer line is kept full of beer, which is the norm, since there is no foam in the line to dry. On the other hand, if you dip the end of a beer tap into beer foam when pouring, a practice I strongly discourage because it is just not proper, the foam can dry within the tap and could cause foaming issues. Beer lines do need to be periodically cleaned. Most bars clean draft lines once every two weeks and this is frequent enough for most beer types.
I wouldn’t worry too much about the draft line issue with respect to beer foaming, but you may want to rethink your frozen beer mug practice, especially after you have used your mug for a beer!