Children can't always differentiate between make-believe and fact, but parents can delay the presentation of evil and doom on violence by turning it off or changing the channel. The Walking Dead may be just fine for older teens who are able to separate fact from fiction and things that can happen from things that are impossible. Younger children have not developed these skills well enough to watch the Walking dead series without negative consequences.
Studies show that watching horror movies or series on television causes a range of negative symptoms that include anxiety, crying, inability to sleep, excessive fear of mostly benign objects or events, constant anticipation of horrific events and nightmares.
Even when children are told that horrific events can't happen in real life, the portrayal of these events on television is enough to convince them that it is possible. Often, a child already has a fear of certain things or events that will be worsened by viewing horror on television or at the movies. Many children confuse sermons about end-time events with things they see and hear on television, including the news.
While it is true that children will be introduced to violence soon enough in real life, it is not good for them to be exposed to constant violence on television. It does not prepare them by 'toughening them up,' making them immune to violence or by showing them that it is 'just a movie.' A child's brain is constantly at work, forming lifelong fears or strengthening their ability to handle anything. Don't feed the fears.