Why does my car shake when I start it in cold weather?

Hi I have a 2003 Nissan Sentra S-ER Spec V and lately it has been cold out because it is mid december and when ever I start my car up cold it shakes a lot and the check engine light starts blinking but this only happens until the car warms up. Would this be caused from my NISMO cold air intake? Also it only blows out heat when I accelerate if I am at idle the car starts blowing out cold air. What could be the cause of that?