As a strictly ordered Transformative, Frostfire will make you a Fox-Morph* (minus the face) before giving Icy Veins. To keep it, you only need fur 'skin' with the Fluffy modifier. Kaithrit are mostly human except for the ears, so they don't have fur. You'll either need to keep the fur or give up on Icy Veins. You can keep the cat theme by using Frostfire, then using Catnip afterward on Arms, Legs and Tail. If you do this, be sure to use the Immuno-Booster after you get Icy Veins to cancel the Frostfire Status effect, or you'll just end up transforming again.
*Kitsune are specifically the multi-tail option, which you have to opt into.
As TheShepard256 says, Thermal Packs are the best way (unless you want something else specifically). Buy a Welcome Basket from Tlako on Uveto Station, then go out into the Wilderness to the Essyra Trading Post, where you can buy as many as you like. They're cheap. too. I actually kind of dislike them because they're so good they invalidate most other options. Shelter Drone is especially useless.
If stacking Freezing Resistance, the thresholds TheShepard256 listed are only true if there isn't a Blizzard. If there is, it's 50% wherever you are. Blizzards don't actually increase the threshold for the furthest areas.
If you're a Mercenary, you can use Second Wind in combat to heal, assuming combat is frequent enough and you can win without taking too much damage. If ranged, you can buy a NaN Deconstructor or Hirudo Devourer from Kattom and heal from enemies.