傘を持たずに出かけた

「〜のに」 means 'even though' or 'despite'. It connects two clauses where the second clause presents an unexpected or contrary outcome compared to what would logically follow from the first clause. It can express surprise, complaint, or regret.

「〜のに」は「〜なのに意外だ」という気持ちを表す。予想外の結果の時に使う。