It's true. Look.
The Walking Dead is a dramatic, character driven show that focuses on characterisation and interaction. It also has zombies. This is often a secondary concern, as the real drama comes from the interaction between the characters and the conflict caused by their different motivations, desires and decisions. The characters move from location to location, looking for signs of life, food, shelter, tools, weapons and signs of walker infestation. They often suffer from severe stress, fatigued, emotional trauma and exhaustion, and their mental health ebbs and flows as a result
Fear Itself is a horror game that creates a disparate group and engineers conflicts between them. It allows you to pull together characters from all walks of life, give them lines to ally along or fall out over and then throw into a stressful scenario.
Within Fear Itself a characters mental health is recorded through the Stability ability. As this drains away and falls below 0, characters start to experience stress disorders - phobias, paranoia, irrational behaviour, hallucinations.
Rick Grimes suffers a massive Stability loss after Lori dies, and succumbs to paranoia and hallucinations as the stress of leading the group alone and the guilt of not being able to protect his wife finally overcome him.
Fear Itself covers this off nicely.
Talking of Stability, Fear Itself allows characters to define a number of Sources of Stability - People, Activities or Innate Traits that give you some comfort and allow you to retain your sanity in trying times.
Lori and Carl were Rick's Sources of Stability. Darryl and Carol found support in each other, Glynn and Maggie found they could give each other solace in another way.
Darryl also maintains a badass facade to keep himself on an even keel, Carl tries to maintain his independence and Rick became a leader. Shane makes Lori and Carl his Sources of Stability, then when Rick returns and Lori and Carl are denied to him, Shane begins his descent into madness.
Losing one of your Sources of Stability - either through death, being disproved or betrayed - is a crushing experience.
We can also look at The Governor - He tried to re-establish some Sources of Stability; Lilly and Meghan and becoming leader of a new band of survivors. When this falls apart,when he sees that Meghan is bitten, he takes a massive hit to his Stability and attacks the prison recklessly and mercilessly. This leads to his death.
We can also look at the character defining moment in Fear Itself - The Worst Thing I have ever Done.
Shane regrets leaving Rick behind in the hospital to die. Michonne feels instrumental in the death of her child, partner and friend. Rick looked for every other way out other than killing Shane.
As an example, let's stat up Darryl as a starting character
Concept: Badass biker
Sources of Stability: Carol, Being a Badass,
Risk Factor: Gung Ho
The Worst Thing I Ever Did: Kill my brother, Merle
Academic Abilities: Natural History 1
Interpersonal Abilities: Bullshit Detector 2, Interrogation 2, Intimidation 2, Reassurance 1, Streetwise 2
General Abilities: Athletics 8, Driving 4, Filch 2, Health 8, Infiltration 4, Mechanics 4, Sense Trouble 6, Preparedness 4, Scuffling 6, Shooting 8, Stability 8
Hit Threshold: 4
By Season 2 Darryl is a General Abilities badass, with extra points in Sense Trouble, Preparedness and Stability (he does suffer a considerable Stability loss during the second season and hallucinates a conversation with Merle). The skills that Darryl Dixon really stockpiles are Shooting and Scuffling, both of which he has in spades by the attack on Woodbury.
Simple, really. Walkers are the only supernatural creatures in this setting, and are both common and familiar.
As such, I would reduce the potential Stability loss of exposure to Walkers by 1 point, and only apply it if the character is taken by surprise or if the Walker is someone that the character was close to whilst alive
Also, you need Walker stats to run a Walking Dead game
Hit Threshold 3
Perception modifier 0
Scuffling 6 (Fist -2, Bite -1)
Tireless. Walkers will doggedly pursue prey until they are destroyed. If the prey is no longer visible, a Walker will continue walking in the direction the prey was last spotted in until they find new prey to distract them
Biter Fever. A bite from a Walker means blood poisoning, septic shock and a painful death, unless the bitten limb is amputated within a number of minutes equal to the characters Health rating. If the limb is not removed before this time has elapsed, then the victim is infected and will perish within [12+ Health Rating] hours.
Headshot. Walkers can only be 'killed' by severing their head or destroying their brain. Targeting a head adds +2 to the targets Hit Threshold, whereas aiming for the neck or eye adds +3 to the Hit Threshold.