bareheaded
From Longman Dictionary of Contemporary Englishbareheadedbare‧head‧ed /ˌbeəˈhedɪd◂ $ ˈberhedɪd/ adjective, adverb DCCwithout a hat or other covering on your head You can’t go out bareheaded in this weather.Examples from the Corpusbareheaded• These kids shouldn't be playing bareheaded in the snow.