I saw this article today which suggests that the reason shrek wears hoodies is because of a large lump on the back of his neck and an actual picture is in the link. Now I’m not going to diagnose what the problem is because I’m not anything close to a medical doctor.
However in the original post I saw there were a few more pictures and one meme where the lump was painted with his face on it. And this immediately reminded me of a movie I saw in the mid-sixties called the Manster. It was about a guy injected by Japanese scientists and he grew a second head.
Anyway enjoy.