They know how to find or kill their own food.
Obviously, the most important aspect of a hunter's survival in the event of a zombie apocalypse will be the ability to locate and kill their own food. After all the stores are looted and/or overrun by walking corpses, the population will need to revert back to hunting and gathering to maintain their food supply. Hunt everyday without ever needing a tag? Hunters will be answering with a resounding: Hell Yes!
Awareness.
Hunters are trackers, they are aware of all the little bits of clues around them. That broken twig, that matted down section of weeds, that flutter on the outside of their periphery - yea, they saw all that while non-hunters are stumbling around waiting for a loud warning or sign. Half the battle of keeping yourself alive in a zombie apocalypse will be staying alert to what's going on around you at all times.
They are resourceful.
Outdoorsmen love to stock up on their hunting essentials and gadgets - but if for whatever reason they don't have them on hand, they'll craft up their own from the scraps in their truck or the sticks on the ground. I know a hunter who regularly tears off the sides of his own boxer briefs for personal hygiene use in the occurrence of a bathroom emergency in the woods. If there doesn't seem to be a way to make it happen- somehow, hunters will create a way.
They have experience in blending into their environment.
An essential life skill in the event of a zombie apocalypse, will be staying hidden. And hunters know all about camouflage. From building blinds with sticks and brush to climbing trees to remaining stealthily still for long periods of time - hunters have a wide range of experience in remaining unseen, unheard - even un-smelled!
Two words: Daryl Dixon
Most Walking Dead fans will agree that the most badass character is Daryl Dixon. I mean, he knocks off zombies with a crossbow without flinching. He pulled an arrow out of himself and then killed a zombie with the same arrow. Besides being a kick-ass shot, Daryl also used his tracking experience to try to help find Sophia ("Sophia!" - Daryl's war cry for all of season 2). Daryl is proof (well, fictional proof at least) that hunters will rule the zombie apocalypse territory.
The sight of blood and guts doesn't bother them.
Let's just be honest, blood and guts will become a commonplace sight in the event of a zombie apocalypse. You'll either need to be able to stomach it or learn how to do so quickly, because survivors won't have the time to be distracted by the sight of a little (ok, a lot) of blood. After the years of gutting, blood trail tracking, and butchering that hunters have done - a little blood and guts won't be much of an adjustment at all.
Spotting.
If a hunter can spot a turkey 600 yards away in a field while driving 70 miles an hour down the freeway, a human-sized zombie is going to stick out like a sore thumb. Early detection allows for an easier, quieter getaway. With a pair of hunter's eyes in your group, you'll be the first to know when it's time to move on before a zombie even catches wind that your in the vicinity.
Aim accuracy.
According to the movies and current literature, there is one sure fire way to kill a zombie and that's in the head. In the heat of the moment, it may be difficult for a survivor to focus, especially if s/he only gets one shot to escape. Hunters are always ready to aim under pressure - they almost always only get one shot to make it count. With practice comes precision - and hunters have been spending most of their free time practicing already.
Access to weapons.
Outside of law enforcement and military, you won't find anyone with more available weapons than hunters. At the start of the apocalypse, hunters will have immediate access to an arsenal of protection within their own home; rifles, muzzleloaders, bows, ammunition, arrows, and gut knives. Not to mention access to all-weather clothing, binoculars, traps, rope, and climbing tools. No looting or searching their local outdoors stores in the event of a catastrophe - hunters are already prepared for surviving on their own.
They watch out for others.
Hunters like to stick together - they know it's easier to get things done when you're with someone else. It's easier to gut and drag a deer with another person, easier to have one person calling in the turkeys while the other one waits ready to aim. Hunters are no stranger to the idea that teamwork makes things move faster, smoother, and more efficiently. Groups that survive the zombie apocalypse will no doubt have hunters among them, they will be the ones doing their best to keep the group working together, well fed, and constantly learning new survival skills.

The moral of this list, if you want to prepare for any threats of an impending zombie apocalypse, it's time to become a hunter. Or maybe marry one...or at the very least befriend your neighborhood outdoorsmen - your zombie apocalypse survival may very well depend on it.