Did Pearl Harbor take place during the Cold War?

No, Pearl Harbor was bombed by the Japanese on December 7th, 1941. It was the end of the "cold war" that the US was waging against the Axis in World War II and the start of their "hot war" involvement. "Cold war" and "hot war" can be used as general, descriptive terms, as demonstrated above. Since this question asks about the Cold War in capital letters it is referring to the tension between the US and the western allies and the USSR and their Soviet bloc between WWII and the late 1980s.