If.. you feel it is related to cold.. and (older) batteries do loose voltage when the temperature drops.. check the voltage of your battery with a multi-meter when the PMP has shut off. You may be surprised.. or be able to determine the PMP could be at fault.
Yea my car is only a few months old so highly unlikely to be a battery issue.
My multi-meter is reading 11.8v at the fuses when my PMP is shut off so it makes sense.