Design and art are not necessarily mutually inclusive. I think Kanye West explained this best in his 2015 interview with Zane Lowe where he said:
"Art is to be free. Design is to solve."
Contrary to popular belief, the visual aspect of design is just but an arm of it. User experience design for example doesn't entail making pretty interfaces. Instead, it's a process of problem solving through various information-based methods. Intrinsically, qualities you definitely need to possess are empathy, problem solving and curiosity. That's what makes a great designer, regardless of industry or application, as far as I'm concerned.
Udacity has a great (free) course on product design which incorporates a lot of UX and design theory in it, I would highly recommend it.