Having the head uncovered without a hat, hood, crown, or other head covering.
From 'bare' plus 'headed,' formed as a participial adjective in Middle English to emphasize the state of having an exposed head.
The Puritans actually made it a point to reject overly fancy hat-wearing, so 'bareheaded' became associated with religious purity and honesty—you had nothing to hide, not even your uncovered head.
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