I was 15 when I discovered Dire Straits (in 1991), and "cool" was the very first word that came to mind. That word is used in various ways (often just meaning "great"), but I always thought Mark was cool in the original sense of the word. I remember seeing him on stage during the On Every Street tour, and he was the epitome of coolness: Just standing there playing all that incredible stuff and barely raising an eyebrow, seemingly immune to any kind of bullshit, not bothered by anything or anyone, a superior being that has seen it all, and so obviously in a league of his own that he had no need whatsoever to show off. That's how he played, that's how he sang and behaved.
Of course his kind of music and style was way out of fashion back then already (not sure it ever was in fashion at all), but cool it was. Most definitely.