For example, if a rover has working temperature range of -70 to +120 Celsius, how does it survive and then restore itself if the temperature drops to -150 degrees for several months?
That is a very good question, and depends on the design. There are in general two ranges for components which are temperature sensitive. The operational range gives the temperature at which the component can be actively used. Within the survival range the component should generally take no harm but may not be actively used. Often what is even more demanding on the components than extreme temperatures is temperature cycling. Mars for example usually has a large amount of cycles, where as moon has the more extreme temperatures, but less cycling.
In principle there are two ways to handle low temperatures for space rovers
Heating your rover so that all the components that are temperature sensitive stay within the respective limits. You can use active heating by for example using energy from your battery. Depending on the battery and your insulation you may not hold out very long though. Radioactive heater units (RHU) are another alternative that can be very effective.
Increasing the temperature tolerance of your system is another option. This can be done by selection of tolerant components, or potentially extending the range of existing components. Usually the most temperature sensitive component is the battery. Insulation is also possible, but may only get you so far.
In general one could say that the thermal design is one of the most critical aspects for space probes, and will often decide about the feasibility of a mission.