Who might find logo design fun AND profitable?
The Doodler
It's the night before an exam. You finally open your notebook to study. Instead of scribbled notes on the Peloponnesian War, you find a rather impressive collection of abstract shapes and swirls. You shrug and hope Wikipedia will provide all the facts you need to pass.
If your papers are filled with little doodles, even if they don't represent anything (most logos are stylized/abstract representations), you may want to consider cleaning up some of those random scribbles.
The Traditional Artist
I had 7 years of traditional art lessons. My art teacher gave me so much knowledge of color and shape. This experience has certainly helped my logo design submissions. A logo design is a piece of art. Many times the client wants a shadow, 3-D effect and you have to know how light would create shadows or the design will simply look off.
The challenge with moving from painter to logo designer is that you must design for the client. You have to balance giving your expert opinion and giving them what they want.
The Digital Artist
Above is a digital painting I did a couple years ago. This was part of my transition from pure, traditional artist to graphic designer. Learning to paint using a touch pad was a challenge but it allows for the easy fix: Ctrl+z. If you are already a digital artist, it would not be a far jump to move into logo design. Just like the traditional artist, you have to be able to work for a client and with the client.
Basic moral of the story: If you are an artist you probably already have an eye for shape, proportion, and color. This knowledge will certainly make your jump into graphic design easier than, let's say, you're friend who's greatest piece of art is a poorly drawn stick figure. This is not meant to discourage anyone who wants to try their hand at logo design. Some clients want something only involving their initials in a pleasing font. If you can tell what looks nice together but are not particularly amazing at painting portraits, you may certainly excel at these logos. But having a background/experience in art has definitely helped me create a wide range of logos.