I can not believe that no one has mentioned the finger amputation scene, so the Doc numbs her up with a local or two and starts immediately cutting? Even the dentist gives it a minute or two before he starts working! But really even in Antartica wouldn't they put you under or at least veil the area before they started cutting through flesh and bone?
She's supposed to be a big-stud marshal, like Rooster Cogburn!
Seriously, it is in theory an emergency situation where she, the only trained LEO, is needed to resolve an ongoing homicide conspiracy that threatens the safety of everyone at the station. So suck it up and just let Doc saw off your pinkies...yeah, right. Doc, of course, has a vested interest in making the amputations as traumatic and debilitating as he can get away with.
The surgery itself is actually plausible. Tissue that frostbitten is completely dead, including all the nerves. I gather that the emergency surgical intervention is more or less cutting off all the black (dead) flesh, debriding the remaining dead tissue and then suturing up the resulting wounds.
That's what it was. He only gave the anesthetic as a precaution just in case some of the nerves were still intact. Most of it was dead but I wouldn't have wante my dr chopping my fingers without number first. There's always a chance that some nerves are alive closer to the actual bone where the needle didn't go. I asked my dr