In the Family Guy universe, Santa Claus really does exist. Not only that, Road To The North Pole explained in great deal, the setting in which a world where Santa Claus is real can possibly happen. It turned out the world was consumed with wanting presents, making the the North Pole into a mass manufacturing dystopia. The details went into how Santa Claus and his elves were able to produce presents for everybody, and the toll it took on the North Pole staff.
Santa just could not keep up.
Unexpectedly, Stewie and Brian ended up taking over Santa's place. This was never their intention, especially after Stewie wanted to go to the North Pole to kill Santa. Despite the desire to murder Santa, Stewie still maintained a surprisingly great deal of innocence. After he waited in line at the mall to see Santa, and got denied, Stewie had a right to feel angry. However, Stewie chose not to carry out his murderous plans, when he and Bryan discovered how the world's entitlement affected Santa. In a rare act of altruism, Stewie attempted to save Christmas, as Santa was in no condition to hand out presents.
Their attempt was absolutely disastrous. As the world awoke to Christmas trees without presents beneath them, they also saw what their collective demands had done to Santa on the news. Brian explained how Santa had deteriorated, and gave a message about how people should restrict themselves to asking for only one present. One year later, everybody followed Brian's request and showed restraint in their Christmas demands. Santa and his elves recovered, and everybody learned to appreciate and accept receiving only one present for Christmas.