From what I have been able to gather from the documentation so far (I am still new to Unreal Engine though do have experience in C++) Character and other classes like it (Pawn) are used to give a physical representation of a entity in the world. So you would use one of those to represent your zombie in your game world.
You would then also need a AIController to do the actual controlling of your zombie. The AIController is where you will place your AI code that controls the Character/Pawn representation of the zombie. A AIController is a non physical actor that can possess Pawn and it’s derived classes and control it’s actions.
So a good place to start would be to look into the Pawn class or one of it’s derived variations which will represent your zombie in the world and the AIController class which will actually control the zombie’s actions.
https://docs.unrealengine.com/latest/INT/API/Runtime/Engine/GameFramework/AAIController/index.html
https://docs.unrealengine.com/latest/INT/Programming/Gameplay/Framework/Pawn/index.html
https://docs.unrealengine.com/latest/INT/Programming/Gameplay/Framework/Controller/index.html