The story opens with a quick overview of Santa's castle in the Laughing Valley. Its focus soon switches to the five Caves of the Daemons in nearby (though unnamed) mountains. These creatures are pagan daemons rather than Christian demons, in that they are not servants of Satan or necessarily evil. Four of the five, the Daemons of Selfishness, Envy, Hatred, and Malice, certainly are bad, but the fifth, the Daemon of Repentance, is a more ambiguous figure.
The Daemons of the Caves resent Santa Claus because children under the influence of his gifts rarely visit their caves. They decide to frustrate his efforts and counter his influence. (The Daemon of Repentance goes along with the plan, since children cannot reach his remote cave without passing through the caves of his compatriots beforehand.) The Daemons first try to tempt Santa Claus to their own vices; they visit him one by one, and attempt to lure him into selfishness, envy, and hatred. Santa Claus merely laughs at their clumsy efforts. (The obvious model for these episodes is the Temptation of Christ in the Synoptic Gospels.) Failing at temptation, the Daemons instead kidnap Santa Claus; they lasso him as he is riding in his sleigh on Christmas Eve, and bind him in their caverns.
Santa Claus is accompanied on his rounds by a fairy, pixie, knook, and ryl, who travel under the seat of his sleigh; once the four realize that Santa is gone, they endeavor to complete his mission and deliver the gifts. They generally succeed, though with some mistakes; they deliver a toy drum to a little girl and a sewing kit to a little boy. Overall, though, they manage to save Christmas. Then they report Santa's absence; the queen of the fairies in the Forest of Burzee knows what has happened. An army of magical creatures is mustered to rescue the missing hero. Meanwhile, though, Santa is released from captivity by the Daemon of Repentance, who has repented the kidnapping. Santa meets the army on its way, and turns it back from attacking the daemons.
(In the seventh chapter of The Life and Adventures of Santa Claus, titled "The Great Battle Between Good and Evil," Baum depicts a combat between massed magical forces. Here in the short story he avoids that spectacle, a strategy he would employ again in the climax of the sixth Oz book, The Emerald City of Oz, in 1910.)

Question: Where does the pixie, ryl, fairy and nook ride when there with Santa? 
Answer: Under the seat of his sleigh
Alternative answer: Travel under the sleet of his sleigh.