Not all zombies are the same. Many works of fiction paint them from anything from re-animated dead corpses to simply virus-driven cannibals.
This is an incredibly important distinction.
A walking corpse is a walking. Freaking. Corpse. It is realistically no threat, because practically any weather will either cause it to rot (warm) or have it become incredibly slow/frozen during cold weather due to lack of body heat. No need for guns or panic. Not to mention the fact that the muscles of the dead will have atrophied and be practically useless. Also, do you know what happens to people who cannot feel pain, like zombies cannot? They die, often quite young, because they don't understand the dangers of simple things (anything that causes pain) and do not seek to actively avoid it.
Now, within the re-animated dead corpse "species" (just humor me with this terminology, I don't think they even classify as anything so I'm just using a familiar term from Biology) you have several different "classes" such as reanimation through magic. Each type will have it's own (massive) drawback. Some will be able to bleed to death, which will eliminate THAT type of "outbreak" fairly quickly through day to day injury. For those that can't, they will likely also sustain enough injuries throughout their daily shambling that their bodies become useless through injury. Hell, they may even succumb to natural disasters or natural predators. If a bear isn't scared of a hunter with a gun, do you think it will be scared of an atrophied corpse?
All of this is ignoring the fact that if all they want to do is eat, they will eventually turn on each other and eliminate the zombie population without any help from our guns.
When you discuss the realism of a zombie outbreak, you have to take into account a ridiculous number of things. But when it all comes down to it, one glaring detail remains.
Zombies are not, and never will be, a threat. There's no "realistic" or "correct" way to approach it, because the job would be done on it's own. That's why the unrealistic scenario is bound to creative works for exploration. It is actually incredibly unlikely that the "horde" would win in this case, because to do so they would have to trump the ultimate power.
Nature.
P.S. Many of these points work for virus-driven craziness too. Feel free to debate them, but keep it polite please.