All the targaryens have purple eyes in the book, that's not just a dany thing. And I don't see how dany could represent ice at all, as far as I know it's either about Jon being stark and targaryen(ice and fire) OR it's about Jon and dany joining forces. Another possibility is dany and the dragons vs the white walkers, or even the fire worshippers vs the white walkers, and with Jon discovering the fire priests and melisandre it's possible that it becomes the meaning.
Or it could just be a broad term of all this fire related shit killing the white walkers
i thought it might be a hint at the "flowery" "poetic" title (suggested by sam tarly) that the arch maester gives his work documenting this present period in westerosi history