The K-13 mountain made its appearance in the Season Six episode, "Asspen", and Woodland Critter Christmas where Stan killed the mountain lion. It is the most dangerous ski mountain in Aspen. The fictional mountain references the real mountain K-12, which is the second largest in the world.
It is revealed by the Old Farmer that the K-13 has a very interesting history behind it. Thirty-five people had died going down it, and a group of students were killed there by a wolfboy who escaped from a mental institution. It was also a burial ground to a tribe of vampire Witchicaw Indians who ate the flesh of children with no eyes.
After insulting Stan Marsh, Tad Mikowski challenges Stan to race down this mountain, and if he wins, the youth center that was supposed to be torn down would remain untouched. During the race, Tad starts out winning. However, after delaying himself by creating various traps to slow Stan down, as well as being distracted by a redheaded girl's breasts, he loses the race, crossing the finish line after Stan had already done so.
After Stan won the race, the spirits of the Witchicaw Indians were set free from the mountain and can now rest in peace.
The mountain appears to be extremely dangerous, with high falls, jagged edges, and trees scattered over the area.