Obviously not from old age, but what happens when a vampire is killed? I know their bodies are turned into dust, but what happens to their soul? Do they go to Coldharbour? I assume that the soul isn't just destroyed, since I've not heard anything on that.

Barring any soul gem-related incidents, I assume that yeah, they become Molag's Coldharbour playmates.

I have never bought into the idea that vampires are bound to the will of Molag Bal.

Personally I think they get what happens to 95% of Tamriel

Dreamsleeve and reincarnation.

Consider that Hircine owns werebeast's souls as their creator and thus they get sent to his hunting grounds. It might be that Molag Bal owns the souls of vampires as their creator so they do indeed go to Coldharbour. But I don't think there's anything in lore that establishes this fully.

I think the only vampires that go to Cold Harbour upon death are the ones that actively worshiped Molag Bal in their unlife like Harkon.

Dead souls go to their aligned AE.

So I presume they would go to Molag Bal as werewolves go to Hircine.

I don't think they are property of Bal inherently. Many vampires like Clavicus instead of Molag. What does AE stand for by the way?

Also, what if somebody worships multiple gods?

I have absolutely no idea, and this is in no way an informed opinion, but I love the idea of the Deadra fighting, really pettily, over someone who worshipped all of them.

Molag Bal: But they're my champion! I made them [censored] that one guy! And they really didn't want to!

Boethiah: Again with the [censored], that's all it ever is with you! Anyway I think you'll find that they're my champion! I got them to kill those sheep so that those giants would trade defective troll fat with that village so that...

Sanguine: Hey, hey let's stop with all this arguing and just celebrate the addition of a new soul to my realm huh? They're my champion, only one ever to out-drink me! Which calls for a re-match!

Azura: After seeing the company they keep... I don't want them any more.

Meridia: Me either

Sheogorath: What's all this arguing about? Is it the nine-headed tiger-rabbits? Oh, hey there champ, coming with me?

Dagon: They most certainly are not going with you they are coming with me, come my champion.

Soul: Do I get a say in this?

Daedric Princes: No!

Cracks me up every time.