I found a Zombie Pigman in the Overworld near my Nether portal. It was grunting normally.

I shot it with my bow and hit it many times with my sword. It didn't take any damage. It was the same even after I turned off my portal.

I was recording at the time, you can see here: https://youtu.be/5csGJNtgUa4?t=20m21s