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