Peter riding his flying legless horse, passing through flames and crashing to a wall is a reference to the arcade game Dragon's Lair.
The racehorses are all named after canceled FOX shows. One bears the moniker The Winner, the title of a short-lived sitcom produced by Seth MacFarlane's own company. Peter's horse, on the other hand, is revealed to be named after the then still-running show 'Til Death, with Peter claiming that he is going to "take that horse and shove it down America's throat."
Peter puts the horse on the roof of his car and slamming on the brakes to get the horse off, this is similar to an episode of BBC's Top Gear where Jeremy Clarkson puts a cow on the roof of a '80s Camaro and doing a reverse J-turn to get the cow off the roof.
While the doctor is going through how long it could before for the gay gene wears off, he starts listing the ways of saying one year, saying "525,600 Minutes", which Peter recognizes from the musical Rent, from the song "Seasons of Love". The musical tackles themes such as homosexuality and HIV/AIDS. For most of society, a man with a vast knowledge of Broadway plays and musicals will fuel speculation of the man's homosexuality.