If you read it a little more carefully, it says "deadly cold," and one зак will be enough.

Okay, let's calculate the approximate damage of a зак on this map. The Demon will be around level 15 by the 3rd week (and your opponent won't let you level up any further). The hero's magic skill will be no more than 5, let's say with magic artifacts it will be 8-11 (this is just fantastic for this map, even if he has a Sar-Iss in the center). So, the damage from deadly cold will be approximately 270-360 HP.
Question: and how will this affect Viti's ballista?! Answer: not at all!