Making snow golems deal damage?

I'm trying to make snow golems deal damage. I've tried /execute as u/e\[type=snowball\] at u/s run effect give u/e\[distance=..1\] minecraft:instant\_damage 01 and other variations that didn't work anyways. Additionally, this doesn't address the fact that undead mobs are healed by instant damage. Is there a way to even do this in vanilla minecraft?