Eh, some DM could decide to make them non-unique. I wouldn't worry.
How about using a similar approach to the one we employed for the White Boar?
A white boar is a creature specially created by deities of nature to destroy some offense against nature, such as an unnatural abomination and the wizard who created it. Legends claim it houses the spirit of a godlike avatar.
The White Boar of Kilfay
The original white boar found around Kilfay was specially created by the Celtic deities to house the spirit of a godlike avatar sent do destroy Shivnar and his bulette-mutation. Other White Boars can exist, with different trapped deities and their own nemeses.
Something like:
Once a mortal creature of ordinary flesh and blood, the ice fiend was transformed into an icy monster when it absorbed the blood of a slain god of evil. The power of the ice fiend varies with the season, it is weakest during the hottest months but waxes to a mighty strength in the depth of winter. Their minds are overwhelmed with a cruel hatred that drives them to kill and torment any living creature they encounter. The fiend only spares a victim if it thinks the creature would cause more suffering if left unharmed - for example, it might let a wyrmling white dragon or frost worm pass unmolested, since these are rapacious creatures of cold.
An ice fiend is 10 feet tall and weighs
X pounds.
The Ice Fiend of The Rrurik Highlands
The original ice fiend was once a ranger from the isolated province of Rjutaffel in Jankaping. Once a champion of his tribe, he slowly grew isolated when the malevolent powers he had inherited began to manifest. After several years he became an ice-fleshed monster dedicated to terror and murder.
Other ice fiends can exist, they may have different abilities depending on what species or character class they belonged to before they transmogrified. For example, a half-orc barbarian may become an ice fiend with rage-based powers who can create a iceax.