Zero is a great character, he's dynamic i agree. I don't think he is really emo, since he has such a strong will, and spirit from what he has gone through. Being emo is surrendering yourself in the sorrow and pain, and be completely blinded by it. He's gone through a serious rough patch the past four years, and trying to suppress something that utterly goes against his nature and who he is, is something that has worn away his charismatic and optimistic attitude, along with seeing his family killed right in front of him, as others have mentioned. He's a private person, and chooses to keep people at a distance because he chooses not to bother people with his issues. Zero has had to grow and mature more than anyone else his age.
Spoiler for continuing...:
He has a cold attitude at times, because getting too close to people would just complicate things, and he is very protective as he knows how dangerous vampires are, and part of his nature is influenced by the vampire hunter clan he is/was apart of, so his first instinct is to follow the guidelines of such. They are trained to keep their distance from people, never to get too involved, and handle their own situations, etc...Plus, I think Zero hides alot of his emotions for Yuki, and I think he is in 'love' with her, I've never seen him more vulnerable with anyone except her, and he is always so protective of her, and it explains why he cares so much for how she feels...out of everyone else. And I do think he does get jealous of Yuki's affection and admiration she has for kaname-senpai, but at the same time he cares for her happiness and safety. And this is based on the anime episodes I've watched. I haven't gotten to the manga yet.