Maybe the tomg was excavated and the coffin sent somewhere else? Where the player gets involved somehow?
Keep in mind, that the files say Snow
Elf Prince, not Snow Prince, and that these two might be different people. The Falmer could simply have a new leader. It seems odd to me, that they would feel the need to add the word 'elf' here (as if for clarification), when everyone already knows who the Snow Prince was.
He didn't have a coffin, unless it simply was no longer there during Bloodmoon, so you could be right. The burrial chamber was empty, save for his armour (minus the helmet) and his spear. So unless they want to make the Nerevarine seem like an idiot, by adding a new door in Jolgeirr barrow that our previous hero overlooked, there was no Snow Prince there, neither dead nor undead.