What does the expression “not to turn a hair” mean and Where does it come from?

The allusion for the expression “not to turn a hair” is to a horse which, though hot, as from racing, has not become sweaty and, therefore, its hair has not become ruffled.

The horsy expression saw literary use first by Jane Austen in North-anger Abbey. When used figuratively it means unexcited, composed, unruffled.