It seems like Goats do not spawn in Frozen Peaks, Jagged Peaks or Snowy Slopes biomes except only during world creation (when the chunk is loaded for the first time).

1. Create a superflat world with Grass as top layer and make it Frozen Peaks, Jagged Peaks or Snowy Slopes biome.
2. Open F3 and check if any passive mob will spawn. (in Snowy Slopes you can see Rabbits spawning though).