i'd start believing seriously doubt it is the cp3, more than likely injectors loosing the prime due to the tolerances being larger than they should be. The truck will start fine in the warm weather unplugged because the metal hasnt contracted. In the cold, it contracts, further expanding the tolerances, loosing its primes and alas, doesnt start because the fuel pressure isnt there to do so. start saving

 

Hey buddy hope this helps i also have 03 if it runs fine after it is plugged in and runs fine all day seems to me grid heater is not working after setting all night solenoid that opperates it could be bad or heater has been removed.Please make sure it is working before you spend any money.