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")