Starting but does not stay running

Ok so I have a 1997 pontiac grand am se with a 2.4 4 cylinder in it. It has 186,000 miles on it and every winter when it gets below 30 degrees the engine will crank and then start but as soon as it hits 1000 rpm the engine cuts out and will not stay running. I have checked and made sure the coils are good and also that the engine is getting fuel. I also tried to have it diagnosed but it does not read any codes so I am woundering what may be the problem with this.
i thank you for considering the question I have submitted and hope to here some info soon so that I may fix the problem or at least have an idea of what it might be.
sincerely
william