Frostbite was a medical condition, which came as a result of exposure to extreme cold.
Zoumas, an alien trader was once left alone in a forest on Burala Prime where he lost several toes due to frostbite. Following the incident, Zoumas walked with a slight limp. (ENT: "Canamar")
Hikaru Sulu suffered severe exposure and frostbite after spending the night on the surface of Alfa 177 where the temperature dipped below 75 °C, below zero. (TOS: "The Enemy Within")
In 2269, Leonard McCoy's hands and face were frostbitten after only brief exposure to Sarpeidon's ice-age atmosphere when he had traveled 5000 years into the planet's past. (TOS: "All Our Yesterdays")
In a deleted scene from "Broken Bow", Hoshi Sato was wondering if she had frostbite after returning from Rigel X. Malcolm Reed noted its symptons as one's appendages blistering, peeling, and turning gangrenous. He noted amputation as a treatment.