It is definitely possible to learn these skills.
What a lot of people get confused with is the difference between Art and Design. In many ways the difference between Art and Design is that Art has no understated functionality. It looks good...because it does. With Design there is usually a reason for something to exist. To be a good designer one must understand what good design is and how to efficiently break the boundaries of logic to create something that works with as little cognitive-load as possible. If a new UI design allows me to perform a task twice as fast as the old one then it is better. If I enjoy the experience of using the new one then it is better.
Of course, there is an artistic side to design, and by using flair and creativity a designer can make better designs.
If you want to become better at designing then there are two things you can do:
- Read everything you possibly can about design. Find the best design Blog's and stick them in your RSS feed. Read through everything you possibly can about design.
- Design something, then design it again, and again, then stop! Now, design something else...
- Learn as much as you can about HCI. There are some great HCI books out there, even past the obvious choices. Read as many books as you can find.
- Join a design community and monitor the work people produce. If you get the chance, collaborate with someone better than you and see how they tick.
I don't know enough about Art to say if you can learn how to become an artist. All I do know is that everyone is naturally creative; you just have to learn how to let it out in your work, that means learning how to use your tools effectively. Once you can do that then you can experiment.
I like to think that many of the standing HCI concepts we use today haven't just come from calculated thinking; more an artistic vision come to life.