Caleb Joe Thomas, 20, and Ridge Scott Dains, 21, were discovered missing on Saturday shortly after 1 a.m. Mountain Time.
Searchers from the prison's Correctional Emergency Response Team and the Idaho County Sheriff's Office found footprints in the snow leading away from the prison.
Thomas was convicted of first-degree arson, grand theft, destruction of evidence and solicitation to commit perjury. His convictions are from Canyon and Payette counties.
He is described at six-foot-one, 186 pounds and has blue eyes and brown hair.
Dains was convicted of burglary in Canyon County. He is described as 5-foot-1, 140 pounds and has hazel eyes and brown hair.
Anyone with information about the whereabouts of Thomas and Dains should immediately contact their local law enforcement agency.