I've never gotten a chance to speak about this matchup but I would like to say a few things.

Since i have zero clue of what sauron is able to do outside of that one scene in the movies, I will talk about the lich king.

The lich king is mighty powerful for a few reasons:

1) his display of frost magic is super impressive to the point where I would be genuinely surprised if he was unable to freeze at least a whole army in a few seconds.

2) his armor regenerates from physical blows, not frostmourne though. Whether or not frosty was destroyed because the sword that destroyed it was light imbued or not I'm not sure. However I wont be including that

3) yes it's said alot and yes it needs to be said more. The raiders who fought arthas were being toyed with until he got bored and one-shot all of them instantly, without delay, without blocking chance, zero conditions. Mind you the raiders were the best of the best. The most powerful champions of the world back then. High tier mages, with spells quite beyond alot in LotR. Death knights with their own necromantic powers. Warlocks, priests, even the warriors and roguss were