The crossword solution for the term 'garment that surrounds 'cowboy hat'' is 'COAT'. A COAT is a type of outerwear garment that is typically worn over other clothing. It is usually made from heavy fabric and is designed to keep the wearer warm. The most common type of COAT is the overcoat, which is typically long and reaches down to the knees or lower. Coats are also commonly used to accessorize cowboy hats, providing an extra layer of protection against the elements.