One thing just about every hardcore Game of Thrones fan agrees upon is this: ice dragons are coming. Although they haven't yet appeared in the books, and aren't guaranteed to, they are referenced enough that fans are convinced they play a part in the wars to come. Most of the information we have about ice dragon lore comes from a 1980 children's book George R.R. Martin wrote 16 years before he released the first A Song of Ice and Fire book. He maintains it takes place in a separate universe, so how are ice dragons made on Game of Thrones? There are a few different theories at play.
The first and most obvious one for the television series to roll with is that ice dragons are made the same way wights are. Old Nan told Bran a bedtime story back in Season 1 that mentioned ice spiders among the wights. So we do have a reference point for animals being turned into undead soldiers. And given that The Night King even managed to zombify giants to join his army, dragons seem like child's play. So one theory is that one of Daenerys' fire dragons dies and The Night King turns it into an ice dragon. That also disrupts the notion that Tyrion is the third head of the three-headed dragon prophecy, making the three dragon tamers Daenerys, Jon, and The Night King (shudder).
However, there's also evidence to support that ice dragons occur in nature, and aren't necessarily made by White Walkers. For instance, in the books, ice dragons are said to be much bigger than Valyrian dragons. Turning something into a wight doesn't magically make it bigger (thank the gods), so this suggests that ice dragons are simply magical creatures that live in nature, rather than zombified fire dragons.
Another theory comes from that 1980 book The Ice Dragon, which features one of the creatures helping a princess defeat seven fire dragons. At the end of the story, the ice dragon melts into a small, cold pond. Some fans believe that the pond outside Winterfell could be a dormant ice dragon, lying in wait to be reborn. These "born not made" theories rely heavily on Jon Snow's own mythology as foreshadowing. He, too, was resurrected from death, which some believe make him the perfect candidate to summon a dormant ice dragon. Plus, since he's a Targaryen, he could actually tame and ride it, joining Daenerys in "ice and fire" — referring to ice dragons and fire dragons teaming up against the Army of the Dead. It'll be interesting to see which direction the show takes with Ice Dragon: Origins, but either way, fans can't wait to see the visual spectacle.