My final essay this last semester for my literature class was essentially about how movies no longer seem to tout themselves as a "tragedy" anymore. A good movie may contain tragic elements, as well as a healthy variety of other emotions, but it used to be that the device was an entire genre in itself in the same way that movies that make you laugh are called comedies. Nowadays, we don't see movies advertised as "tragic" very much, if at all.
I don't know how War Horse ends and so I don't know whether it's technically a tragedy, but it seems like it fits the genre better than anything to come out in a long time, and it's nice to know that the form isn't dead entirely, even if it's not marketed.