For hypothermia and frostbite, when do they amputate your limbs and how long does it take for them to know?

Quite a while: Frostbite injuries are classically very slow to declare a correct amputation level. What initially seems to be non-salvageable can heal remarkably but slowly. The general rule is "injured in january, amputated in july.".

Requires an exam: Mild frostbite heals well, even blistering can heal without disability. Severe frostbite usually takes days to demarkate, and sometimes weeks. As long as it is not infected, the injury can be treated supportively until the determination is made. If infection occurs, then the issue becomes more critical.