While the Night King turning Viserion into an ice dragon may have been one of the coolest things ever on Game of Thrones, it also does not bode well for the living's chances in the war. He's going to do some major damage, and Daenerys' team should start working on defensive strategies. Can ice dragons be killed on Game of Thrones? The answer may have been revealed in the episode itself.
In Sunday's episode, Jon sliced up a White Walker and noticed that all of his wights except one dropped dead — much like (excuse this reference) the droids in The Phantom Menace when their control ship is destroyed. As the team only needed one wight, that was a little too convenient, but allow them that coincidence. The explanation given wasn't delivered with much grace either, but it does present an interesting set of stakes for the upcoming war.
Jon suggested that perhaps the White Walker he killed had been the one to turn those wights. Beric Dondarrion supported that claim, later theorizing that all of the White Walkers and therefore all of the wights would drop dead if they took out the Night King, because he turned all the of White Walkers. It would be a chain reaction of death.
The team couldn't risk killing any White Walkers before Daenerys got them out of there, because they couldn't risk their captured wight dropping dead. However, once the wight makes it to King's Landing and the meeting with Cersei is over, this is going to make conquering the army a lot easier. This theory of Jon and Beric's also suggests that once the Night King is gone, Viserion will fall as well because he's the one that turned him.
It's also extremely possible that dragonglass and Valyrian steel can kill an ice dragon the same way the two magical materials easily defeat White Walkers — unless some kind of House Targaryen connection renders them invincible.
As stabbing would require getting super close to the dragon (pretty impossible) or acquiring the Night King's Olympic-level javelin throwing skills, the easiest way to remove V-ice-serion from his new rider would be to borrow Cersei Lannister's giant crossbow. Unfortunately, it's doubtful that the Queen would just give up her secret weapon to Daenerys and the Northern armies just like that.
All that said, the undead dragon is probably here to stay for a while. Even with multiple ways to take the beast down and kill him for good, the Night King's army presents a large and immediate threat. Slaying this dragon is not going to be easy.