The red veins that appear on one's nose after years of righteous boozing. The veins may be accompanied by pocks and vodka filled bubble busters that fester on your face until you dunk them in holy water.
See: Ted Kennedy, Tip O'Neill, Tommy Lasorda, WC Fields, Fred Mertz, or any commie politician who wakes up with Popov in his coffee. Boozenose is a mark of honor that can only be earned. If you take offense, too bad. You should have out down the cocktails a long time ago.