The phrase describes a person exhibiting a brash and carefree attitude that feels inappropriate or out of place. This behavior is reminiscent of someone who has chosen an uncomfortable experience, like a cold bath, over a more pleasant alternative, like a hot bath, highlighting an element of recklessness or folly in their choice. The analogy suggests that while they may appear confident, the underlying decisions reflect poor judgment.

This characterization captures the essence of a person who seems to flaunt their carefree demeanor despite the discomfort they might be experiencing internally. Wodehouse cleverly uses this imagery to convey the idea that sometimes people put on a brave front, masking their insecurities or discomforts behind a veneer of jauntiness, which can come off as offensive or grating to others.