Do not bother attempting to use Barrage or Artillery to destroy the fence. It will not work.
Find different routes for avoiding barbed wire when using Zookas.
If you have to go through the Barbed Wire, instead of using Zookas use Tanks.
If there is only a single row of fencing in a select area that must be crossed to carry on an attack, place a Medkit on the Barbed Wire as Troops pass through. Examine the heal per second of your own Medkit before attempting as having a net loss could result in a failed attack.
Barbed Wire was invented in 1865 by Englishman Richard Newton.
It is the only building that cannot be destroyed.
Troops that happen to come in contact with the Barbed Wire will turn a bluish tint until they cease taking damage from the fence.
The blue tint may have come from the Cryo Bomb's effect, where everything inside the blast radius turne blue-tinted and slows down.