I'm just making a simple farmhouse, not much too it. However, all the chickens and the cow I put can walk through the woven fences behind the house. Do I need to do something besides just place the fences to prevent this from happening?

add some animal idle markers inside the area and set to the NPCs some AI package sandboxes with tiny radius, maybe just to cover the area where the fences are.

You will most likely need to put some primitives in over the top of the fences which cut the Navmesh.