Why won't my car stay running when it is cold?

I have a 2000 cougar, v6, 2dr coupe as well.  It also misfires, rpm fluctuates when idling, and stalls.  It only does this when it has been very cold out for about 2+ days.  It has been going on for 3 years now.  I recently had the fuel pump replaced, thinking that would help. It didn't   I thought warming up the engine would help, so I have tried getting engine temp up to where it normally runs.  it still stalls out at every stop sign and stop light.  Only thing I've been able to do is pop it into Neutral and keep engine at a higher rpm & then drop it into gear when the light changes.  This can't be good for my car.  I don't know what to do!