Let's see. Dragons… check. Magic… check. Ancient gods and talk of prophecies… double-check. Yep, A Clash of Kings is fantasy. But before we dig into this a bit, let's sort out why it's a war drama, too. Not to blow your minds or anything, but the plot is pretty driven by war in this book, so while we spend a whole lot of time off the battlefield, A Clash of Kings is definitely in this genre as well. But now onto fantasy.
We don't suppose it is any surprise for you that Martin's novel falls under fantasy, a genre famed for its use of supernatural or otherworldly elements in constructing its plots and settings. Dragons are usually a good indicator.
But there are other elements of the novel that point to the fantastical, too. For starters, the entire history of the world has been created from scratch and truly impassioned fans could probably write a history textbook on the backstory's rich detail. It is also impossible in our reality for summer or winter to last for ten years during one seasonal cycle, for more than a generation in another, and then less than ten in another. The entire concept ignores this little thing scientists call physics—and throwing science out the window is a classic fantasy move.
If you're looking for a specific classification, A Clash of Kings might be shelved under the subgenres medieval and epic fantasy.
Medieval fantasy takes a medieval setting and blends it with the supernatural trappings of fantasy. Martin based a large part of his world on the Middle Ages, specifically the Crusades and the Wars of the Roses. As such, his society contains the trappings of kings, knights, and chivalry, but places them alongside fantasy motifs like sorceresses and ice zombies.
Epic fantasy is defined as containing "a life and death struggle between good and evil, a large cast of characters, and multiple books." A Clash of Kings definitely has a large cast of characters, and Martin has suggested the series will conclude with seven or eight novels total.
The difficulty with putting the novel squarely in the epic fantasy box is the "struggle between good and evil" part. Few of the characters we've really gotten to know have been entirely good or all evil. Stannis is kind of a jerk, but then again, he does have a point that the Iron Throne is rightfully his; Jaime may have tried to kill Bran, but he did it to protect Cersei, whom he loves. Arguably the Others are pure evil, but since they are still shrouded in mystery, we can't say for certain how that will play out.
The thing about genres, though, is they aren't exclusive clubs that require their members to dress and act exactly alike—they are more like soft guidelines, requiring members to share certain traits but with the flexibility of self-express. As such, we feel we can mark down A Clash of Kings as epic fantasy with little worry. Besides, war's pretty epic in its own right.