The Cold Prince is imprisoned on the Frozen Isle of the Banished Usurper in the Prison Palace of the Cold Prince. As long as any of his thirteen children live, there is a chance one of them will help him return to the mortal realm and cast it into eternal winter.
To defeat him, either:
Kill all thirteen of his children.
Collect the magical cold-iron weapons that were forged by the ancient dwarves of old under the direction of the Eilvalorians.
These weapons are secreted away within the hidden treasure vaults of the Eilvalorian Princes.
With these weapons, the immortal Cold Prince may be slain.
One must travel into the Realm of Faerie to do so.