Lannisters aren't allowed to have valyrian steel weapons. Thus Ice is given to Payne rather than immediately sent to Tywin to wield himself, and then, clearly, Jaime, and therefore Joffrey, aren't Lannisters so they can own them.
Meanwhile, every Stark in the current story will own a Valyrian Steel weapon... then die.
Ned...
Technically Rob owned Ice, til he died.
Cat owns oathkeeper while she owns brienne... she's already dead lol... but probably about to release brienne... and then die again.
Which puts oathkeeper back on the path to Sansa.
Bran is about to inherit bloodraven's position, and presumably Dark Sister along with it.
Jon... yeah.
Which leaves Arya and Rickon as the only ones that aren't clearly headed to or already are owning valyrian steel.
Arya will end up with one, and then of course she'll die.
Rickon will be left, and with the full power of the true Northmen, who would never forget the thousands of years the Starks have taken care of them, will recover the north and become lord of Winterfell...
and the final epilogue will be an "unexciting" short scene of Rickon receiving the blades made from Ice...