On its own, Cold subtype is not a net advantage to an adventurer. Fire effects are too common. The risk of getting raked by Fire damage is very high unless you can get a Ring of Major Fire Resistance or similar magic.
I agree that a ring of this kind would be very valuable. But the downsides are great as a permenant effect without stacking with some other kind of defenses.
Balancewise, you should as a DM should assume the PC will eventually get a Ring of Minor/Major Fire Resistance eventually, or stack it up with some weirder defense. Is that going to be a problem?
My guestimate is this effect is roughly as valuable as a Ring of Minor Cold Resistance. Not taking a slot is neato, but being permenant has some significant downsides, too. I would put the price in the 15k-20k range.