Ok, here's my take on it.
Freeze is a Cold-Based attack, but per Cold-Blooded, the +4 technically only goes to Damamge, the way it is written.
So, me personally, I would not make the Stygian make an AR save vs 4 every turn, as there is no actual damamge to increase due to Cold-Blooded. However I would increase the Strength of the Freeze by +4 per Cold-Blooded from 12 to 16.
That's how I would play it.
SP