[2023] I have pelted Anti-Santa 50 times

You should only need to actually successfully hit him 10 times. There's a few things that might be the problem here:
- Your ability to throw snowballs is loosely tied to your ranged level, so you may not hit him every time.
- It is quite easy to hit players rather than anti-santa if the world is busy. It didn't look like it was the problem here.
- You need to stand on firm ground when the snowball lands so you can hear what Anti-santa has to say about it. If you're sliding you'll have to throw another one. You don't actually have to be on the field to pelt him. You can stand outside of the fence and get it from there.
- Once you get to the final snowball to land, Anti-Santa will tell you to stop. Listen to what he has to say and the chat that comes after. You will only be able to send Anti-santa flying once Jack Frost has made you denser. (And attacking from the west yields the most spectacular result)
Given Jack's chat, you're not too far off!