My maiden aunt, Honoria, always alleged that she called off her engagement to a wizard in the Improper Use of Magic Office because she discovered in time that “he had a hairy heart”.
We don't know if these hairs serve any purpose themselves, but the follicles vellus hair grows from are essential banks of stem cells that repair damaged skin after injury.
Though somewhat dated, the expression “to have a hairy heart” has passed into everyday wizarding language to describe a cold or unfeeling witch or wizard.