You say -17oC to 0oC, but the chart seems to indicate as cold as -40oC; which is correct?The performance of components like electrolytic capacitors will significantly change at low temperatures.Battery performance, even with Lithium Ion batteries, will likely suck.A GSM module has quite a high short term peak current requirement and will need a good supply; will a cold battery cope?The voltage in the chart rising to 5V may be an indication of a flagging battery. If the supply to the Nano falls below 5V then the analog reference will also fall below 5V and may therefore make your calculated analogRead value go up.Do you have a link to the exact BMS since it is not clear what it is.Suggestions:If you can, monitor the voltage level from outside of the cold space using a multimeter.Alternatively, go low level and configure the ADC registers manually (instead of using analogRead) and use the internal 1.1V band-gap reference as the analog reference. You'll need a voltage divider to bring the input voltage into range.
Would you recommend to change to Nimh battery?
Most SIM modules are designed to run from a single Li cell, and the Arduino will run on one too. Get rid of the converter (which may not be able to supply the peak current required by the module) and use your cells in parallel.
...this sim module needs a supply between 3.8 and 4.4v, otherwise does not work.
Which SIM module (post a link).Did you understand the part about the two diodes in series?See this diagram, top/right.Leo..