No animal has shown symptoms so far. There are plenty of diseases that infect humans but not animals and vice versa.

The governor was great but they dragged that story out way too long. That horse died last season yet TWD won't stop beating it.
I suspect they're recycling this plot to save money. That's why they were on a farm forever with nothing happening in season 2.

They've slaughtered main characters during the first 3 seasons. Just because they all narrowly survived during the first 5 episodes of season 4 doesn't mean they're safe. Plus, Carol's gone, unless she returns at some point, but that's speculative.

Hot! They can double date with Hershel and Lizzie. When Carol comes back she and Carl can get together too. Stat isn't a crime when there is no government.

In a zombie apocalypse people in their 40s wouldn't breed because the risk of a zombie fetus would be too high. Social norms would change to encourage people to have kids in their 20s.