cold starts

Best way to check this is to test the 'start' signal from the ignition switch to the starter solenoid. You should get 12 volts to this wire as soon as your turn on the key. If so, then most likely you need a new starter assembly. If you are not getting the 12 volt signal, then the ignition switch needs to be checked.

I have one too. The starter motor has a solenoid that gets corroded...and in the cold - the solenoid is stuck....changing the battery sometimes works for a short time...until the corrosion is too much....both the starter motor and battery fix the problem permanently.