LORELAI: And we’re Ernest Builds a Snowman.
Lorelai is referring to the Ernest film franchise, starring Jim Varney as a well-meaning simpleton named Ernest P. Worrell. The films came out of a series of advertisements in the 1980s, which then became a television sketch show, then a series of low-budget films, beginning with Ernest Goes to Camp in 1987, and ending with Ernest in the Army in 1998 (by this stage, the films were going direct to video). The films were not critically well-received, but quite profitable.
Although Ernest doesn’t seem to have built a snowman, he did have a winter-themed outing in Ernest Saves Christmas (1988), generally considered one of the best of the Ernest films.
The Annotated Gilmore Girls 