A hat or cap includes a main hat portion and an outerband or fold-down portion secured to the main hat portion in a manner that permits the outerband to be moved upward and downward with respect to the main hat portion from a first position, in which the outerband lies over the main hat portion and away from the wearer's face and eyes, to a second position in which the outerband covers and protects a part of the wearer's face including the eyes. A lens or goggle portion, which is integrated into and attached to an opening in the outerband, is positioned over the wearer's eyes when the outerband is in its second, lower position.