The dragon died though. It's a dead dragon, reanimated by the night king. I don't think dead things can breed.Anyone hoping Viserion and the dragon connection with Targaryans somehow prevents him from killing his brothers and Danny and they lay more eggs? Maybe you need ice and fire to breed dragons and that's why they all died out / stopped laying eggs? What if fire and ice and sex with a raised from the dead dude is the only way Danny can have kids?
It's an ice dragon because it's a wight, not because it's a special breed of dragon that breathes ice.