It wouldn't be happy, but it should still start in fairly cold weather without the grid heater. You might check your lift pump and see if it's working properly. These were notorious for going out because they had to work so hard to try to suck the fuel from the tank rather than push it. They were changed to an in-tank style in '05 and they sell a retrofit kit to change the '03-early '04 trucks to this style. If it's working ok then it sounds like the signs of injectors headed south.