The floor was made of cobblestone slabs placed on the higher half of the block, and it was on a platform over an ocean biome. They'll look towards you, but they won't move whatsoever, including if you were to try and make them breed. 

Steps to Reproduce: 

1. make a 10x16 birch oak fence in an ocean biome

2. make the floor out of slabs, on the upwards half of the block. 

3. move two cows into the fenced area.

4. they might still move around. if so, simply unload and re-load the chunk.

Observed results:

Cows will stand there, not walking in any case, even if you attack or try to breed them. They will, however, move their heads. 

Expected results: 

 The cows walk freely within the fence and act as they would anywhere else. 

UPDATE: I fixed it by replacing the cobblestone slabs with dirt, and it works fine now. This took place before I thought to grab a screenshot.