You know, I've wondered about that myself, which is what led me to taking a part of it to a topic. I reckoned that, being that he was brave and adventurous in Link to the Past and the holder of the triforce of courage in Ocarina of Time, that a cute, cuddly rabbit would be one of the last things he would be. Of course, we are talking about the heart, but rabbits are low on the food chain and are most notable for two things: being prolific and running away. I guess it was saying that he was a softy inside?
And what's so good about my opinion? ;p Well, to me, that doesn't sound like you, no. I would say that you are nocturnal, or at least someone who prefers the cover of shadows; you may also wear something that keeps most of yourself concealed (which is probably dark in color), at most all except for the space around your eyes. Otherwise you seem like a normal kind of guy on most occasions, though there is definitely a feeling that people can pick up about you if they get close enough, and in the light they may even see the space around you dimmer than normal, both of which warding off most people aside from those who have greater amounts of curiosity, innocence and good will. Your eyes are different colors; one seeks to draw something special to you closer while the other keeps an eye out for what you (and perhaps others) can do without. However, when you're only in the company of those that you have accepted, do you appear a lot brighter, open and less serious (depending on the occasion, of course). For those that earn your wrath, I can imagine yourself enveloped in dark flames or, perhaps, consumed by them until the only defining feature is your eyes, like you had mentioned. Other than that, I see you as a lot more approachable than you do. Of course, keep in mind that I'm working more with symbolism than observation.