This episode is a Christmas spoof of Washington Irving's Halloween novel, "The Legend of Sleepy Hollow".
When the Headless Snowman melts, he makes reference to a line from The Wizard of Oz (1939), saying, "Oh, I'm melting! Oh, what a world!" just like the Wicked Witch of the West.
In the end they said that William Fagen Higginson was the "richest man in town." This echos a line from the Christmas film, It's a Wonderful Life (1946). In that film, George Bailey was rich in friends. In this case, Higginson was rich literally as well, since he had just found his ancestor's missing gold.