From what I'm reading online, a cat is pretty likely to need direct veterinary intervention for a good outcome. Apparently infection and wound biting are likely problems you'll run into. If you can't afford to treat a stray, a local shelter might be able to do more. If that's not a viable option either, I think you'd at least need to plan on some kind of antibiotic treatment to prevent or treat wound infection as tissue falls off and a safe form of pain intervention. Cones seem to be useful in preventing chewing/licking that will complicate healing.
Useful link:
https://evcc.com/blog/frostbite-in-cats-highland-in/