This command isn't working in version 1.12:
/summon minecraft:zombie ~ ~1 ~ {ArmorItems:[{},{},{}, id:"minecraft:skull",Damage:3,tag:{SkullOwner:MHF_Wither}}]}
What's wrong with it?
Most items in commands need to be set to a count of 1, otherwise they have the standard amount of 0.
This is the working command:
/summon minecraft:zombie ~ ~1 ~ {ArmorItems:[{},{},{},{id:"minecraft:skull",Count:1,Damage:3,tag:{SkullOwner:MHF_Wither}}]}
Count:1
.{
with a space. But since my solution worked for you, you probably didn't do that in the game.