MELISANDRE'S PROPHECY (WHICH MAY FORESHADOW ANOTHER ARYA KILLING)
The final big hint that Arya would be the one to take down the Night King came from Melisandre, who is (as everyone knows) a big fan of visions and prophecy. Not all of hers come true, of course - she failed miserably at predicting who would be Azor Ahai - but when she first met Arya back in Game of Thrones season 3, she seemed to predict Arya's biggest kill (so far).
The Red Woman looked at Arya and said "I see a darkness in you, and in that darkness, eyes staring back at me. Brown eyes, blue eyes, green eyes, eyes you’ll shut forever. We will meet again". She reminded Arya of this in "The Long Night", and it seems that she was right about this one. The brown eyes that Arya shut are probably those of Walder Frey (although she's killed so many people that plenty others are sure to have had brown eyes as well). The blue eyes, of course, belong to the Night King; other characters in the series also have blue eyes, but the blue eyes of the wights and the Night King are a defining feature that Melisandre even killed out.
This has led to some new speculation, of course. If Melisandre's prophecy is correct (for once), then who is the green-eyed victim still to come? The most obvious choice is Cersei herself; she's green-eyed, a major player, and on Arya's kill list. Melisandre may be wrong, of course, or she could have simply been predicting the sheer volume of people that Arya would end up slaughtering, but this may well mean that Arya is on her way to taking out every big bad in Game of Thrones... although whether that would make fans happy, or just be a little too perfect, is yet to be determined.
Game of Thrones continues Sundays at 9pm on HBO.