I still have a feeling physics would do its job pretty well if an ice dragon scooped up a White Walker, crushed it in its jaws and swallowed it into its stomach.
We're not sure of the affect dragonbone or dragonteeth has on Walkers, so maybe they'd just die anyway.
In the books fire is meant to disdain Walkers, even though the show ignored that completely, I think dragonfire would melt them, being the hottest substance on earth. Personally I think the Walkers use ice magic as a form of preservation, because look at the Night's King and then at the normal Walker, they're very different looking, since the Night's King looks smooth, while the other has folded skin sorta kinda, so maybe since the Night's king can turn babies into the semi-immortal Walkers, maybe he can preserve himself better than the others.