2001 Pontiac Grand Am it wont started in a cold wheather

When the problem occurs, if it is no crank or slow crank, I'd still have to check your battery and cables.

You can use a digital volt meter take a reading across the battery posts, with everything turned off, around 12.6 volts is considered a full charge. With the leads still hooked-up have a helper turn the key to crank, the reading should drop some, but not below 9 volts.

When the problem occurs, if there is no starter action, you may have to get at the terminals on the starter solenoid. The purple wire goes to the S terminal on the solenoid. It should be hot with the key in the crank position. Also check the field terminal, goes from the solenoid into the starter housing, that should have good voltage, with the key in crank position.

Have you tried cranking in neutral, when the problem occurs? Any testing, make sure the tranny is in park or neutral and the e-brake is set.