This is an original US mountain troop ski cap. This type of cap was made specifically for US ski troops during World War Two. It is considered the second pattern, it replaced an earlier version of the ski cap that had a chinstrap that was connected to the side flaps. Also, two ventilation grommets were added to each side with this version. This second pattern of the cap came into use in 1943.
These hats are most known for their use by the famed 10th Mountain Division during WWII. During World War Two, the 10th Mountain Division spent time training at Camp Hale in Colorado. After their time in Colorado, they spent a little time training in Texas at Camp Swift before being shipped overseas to Europe. When they arrived in Europe, they were sent to the Italian campaign were they engaged in heavy fighting in 1945.