The episode title refers to the 1944 song "Baby, It's Cold Outside" by Frank Loesser. It was popularized in the film Neptune's Daughter (1949). As of 2020 there were over 400 known recordings of this song, including one featuring 'Family Guy' creator and voice actor Seth MacFarlane.
Stewie calls Brian a "son of a bitch." As a dog, he literally is a son of a bitch.