Um, no? Zatanna has ties to Bruce when they were younger, sure, but it's not the same thing. Does Zatanna have a book that is considered, by the company of DC itself, to be in the Batman Universe? Is she involved in every single crossover event between all the Batman books? Does she sometimes appear in a book that's title is "Batman & Zatanna"? Has she ever, for long periods of time, lived with Bruce and gone out to fight crime with him specifically? No, but Red Hood has, for all of those things.... I'm not saying Red Hood isn't in, but it's just wrong to say he isn't directly considered, by DC themselves, to be a member of the Bat-family, and therefore considered a large part of the Batman universe specifically. Zatanna is not. And considering the New 52, she and Bruce don't seem to have the past they did in the old continuity. Red Hood is just as much a Batman specific character as Robin, Poison Ivy, etc. Like I said, maybe he's in, maybe he's not, but the fact that he's specifically Batman can't really be denied.