Frozen Variants should burn in The Nether

Considering that The Nether is designed to be a dimension with a hot climate (and surrounded by lava, no less), I find it strange that Strays and the new Frostbites, which are literally cold creatures, do not have the slightest reaction upon spawning or teleporting to the Nether. It would be a nice touch of detail if they were to burn from the spiciness of that realm.