Could be lambda sensors mines a 1.8 and did roughly what you described would try to die on cold start and hunt badly coughing and misfiring and then would sort itself out. If it is fine when warm could be an idea just to get a couple of second hand lambdas see if it sorts it. Have you had the EML on recently? Car relies on closed loop fuelling a lot more on cold than warm and on startup. You'd never think lambdas could cause cold start issues but they can.