My daughter and I thought the same thing. We knew no one had hit it with a sword, so we think the arrow did it. At the velocity at which it was coming from the crossbow, I think it could cut the horn in half!
G'nad is right on with the placement of the arrows, but I think I figured out when the horn was split.
After the 2nd arrow, Boromir drops to his knees. Close up of a sweaty, exhausted, dying Boromir. He is attacked. He rises up. Camera catches him mid-chest and up. He does battle with an Urak Hai. The third arrow catches him. Then, we see long shot of Boromir with the horn split.
Even though we don't see the result of the battle with the last Urak Hai because of the camera angle, the horn is split during this battle. Also because of the camera angle, we never see where the Urak Hai's sword goes, etc.
The third angle could have split it... but I don't think so. I think it was the last sword play Boromir has with the Urak Hai. When the third arrow hits him, Boromir could not stand back up. Bleeding out, he can't go on.
That's what I think... but I think it is ambiguous at best.