No -- interventional nerve destruction, no matter what the means, is never permanent. Nerves grow back, at a rate of about 1/2 inch per year.
I don't know.
But, I've heard over and over that when people get radio frequency ablation (a procedure where the nerves are actually BURNED by radio waves), the nerves grow back! And, sometimes they grow back and cause WORSE pain than before (and the patient wishes they never had the procedure done). And, sometimes the nerves grow back so slowly that people sing the praises of Radio Frequency Ablation, and some times the nerves grow back and people go back and get the procedure done again in a few months.
I would *guess* that "nerve freezing" would have similar results?
Go on to Google. Here's how I do "searches" to get answers to procedures I might need done. Type these search phrases (no quotation marks):
nerve freezing
nerve freezing experiences
nerve freezing results
nerve freezing stories
nerve freezing problems
nerve freezing success