I was playing around with name tags and leads. I wanted to attach a snow golem to a lead. Before I did, I noticed that it was not making a snow trail. I ignored it and named it "Snow Golem" with a name tag. I attached it to a lead and flew in the air. I unhooked the snow golem in the air and it fell down. It didn't take any fall damage. I could still kill it by attacking it with an empty hand. I made another one, this time not naming it, and tried to make it die from fall damage again, but the same happened; no fall damage. I killed it and reloaded the world. tried to kill it with fall damage again, but no damage.
It still shoots snowballs at other mobs.