Deadly cold always kills one creature. Therefore, it will take down a ballista in one go.
Ugh, I've gotten really bad. What kind of a fool am I, thinking a ballista can be affected by area-of-effect spells?! You can only kill a ballista with area-of-effect spells that are not area-based :D However, you can kill a ballista with a ring if it has the "Deadly Cold" ability.