Refers to having sex with a girl on her period.
The definition refers to the cold war fought against the Communists who commonly used red as their primary color.
Similar in meaning to "Getting your redwings"
Joe: "Hey Tim, what happened last night after you left with Mary?"
Tim: "Oh man, it was nuts I ended up fighting in the Cold War."
"Jill, have you ever let anyone fight in your cold war?"