Cold-drakes were, to the best of our knowledge, lesser dragons; those of dragon-kind who did not have the ability to make fire.
They were used by Morgoth in the wars of the First Age, though no specific mention of them in this period remains in Tolkien's published work. After the War of Wrath, in which most would have perished, some few seem to have escaped into the northern regions of Middle-earth, beyond the Grey Mountains.
As the millennia passed, their numbers grew, until they became a serious threat in the later centuries of the Third Age to the Dwarves that mined the Grey Mountains. In the year 2589 of the Third Age, Dáin I, King of Durin's folk, and his second son Frór were slain at the gates of their halls by a Cold-drake. The attacks of these fearsome creatures persuaded the Dwarves to migrate eastwards from the Grey Mountains, and it was soon afterwards that their realms in the Iron Hills and at Erebor were established.
Of the history of the Cold-drakes after this period we are given no hint. Four hundred years later, at the time of Bilbo Baggins' journey to Erebor, they seem to have left the Grey Mountains (at least, Gandalf makes no mention of them when describing the dangers of that region). It is possible that the Orcs who colonised the Mountains after the departure of the Dwarves drove them back into the cold wastes to the north, but we can do no more than speculate on their ultimate fate.