If you're searching for a Museum of Winchester History in Idaho, you won't find one—because there is no city named Winchester in Idaho. This appears to be a case of mistaken geography.
Several possibilities might explain the query:
Idaho offers rich historical preservation through the Idaho State Historical Society, which operates the Idaho State Museum (Boise), Old Idaho Penitentiary (Boise), and supports county museums statewide. The Museum of North Idaho (Coeur d'Alene), Bonner County History Museum (Sandpoint), and Bannock County Historical Museum (Pocatello) are among many legitimate options.
Before planning a visit, verify the correct location and institution name to ensure you find the history you're seeking.