Most of the meats that reach your table today are raised commercially. Big operations where cattle, chickens and turkeys, are kept confined, and fed special diets, given shots for health then slaughtered, processed and shipped to stores, to be purchased by you.
What would happen to the animals if the SHTF and the human component of the operations ceased? Naturally, Preppers would consider the farms to be a source of food, but others would as well and a wholesale slaughter of these animals may happen quickly, because for the most part the animals raised commercially are not allowed to roam free and graze. They are penned up; fish in a barrel if you will, and even inexperienced hunters could manage to kill a few dairy cows and some beef cattle.
Unless you live close to a farm of this sort, you would not be able to take advantage of the situation. Most people would not know how to slaughter an animal correctly, so the waste would be immense. Many of the animals would die from dehydration, and starvation, because no one would be there to tend to them. Even if the animals were set free, many would die because there probably would not be enough grass for grazing and there would be limited water supplies for large herds.
Ones that have long-term survival in mind would, of course, gather a few of the animals to start their own farms. This would, of course, require land, experience, feed, and water supplies.
There are horse farms, as well, and if the crisis was extended, then horses may be the only mode of reliable transportation, so keep this in mind if you live close to any farms that raise horses. Forget about trying to corral wild horses for transportation once the SHTF. This would require extensive experience and time to break wild horses to the saddle or pack.
Animals would die and those in the zoos might escape, or someone out of sympathy may let them loose to create havoc in the local communities. Most of the animals would not survive long out of the zoo. Certain reptiles may adapt and create problems similar to the python problem in Florida.
Some of the reptiles could cause you problems, as well. Exotic snakes may live long enough to bite someone or some animal and if they live, they may begin to change the ecosystem in the area.
Large predators would cause problems as well, in the short term. Lions and tigers, for example, would seek out domesticated animals first for their meals, (the easy kills) and then hunt for wild game, which could cause you problems either way.
The fact that you live near a zoo may not raise any red flags, but in the event of a catastrophic event, there could be problems.
Right now, you can start to map out where the farms are, where animals are raised so you can take advantage of this food source during a crisis if the farms are abandoned or the owners die because of the crisis.
For most people, animals from local zoos wandering around will not pose a great threat, but it is certainly something to keep in mind once the SHTF.