I voted no but I have a synesthetic friend who would disagree. In a sense, the keys have different "colors" to me. D-flat major is sea green, F major is sky blue, D is bright red, for example. I don't, however, see these colors as I'm listening to pieces as they play—even "simple" pieces use so many chords that it would look like fireworks in my head. I think the colors have come about because of a visual association with a sentinel piece in that particular key. Fun to think about but not practically useful at all.
Choosing the home key (for me) depends largely on the instruments and their ranges. I can evoke any feeling or emotion using any key, so I don't buy into the key psychology stuff. Not saying it isn't true—it's just not true for me. I often modulate in unexpected ways in most of my pieces (some longer works can go through a dozen key changes) but generally find my way back to the home key. I find that how the different keys relate to one another is the most important factor in choosing the mood for the work!