Cold starting problem

you could have a couple differnet issues. cold start misfires, an intake air leak, poor compression with engine cold,or a fuel pressure issue with a leaking injector or fuel pressure is bleeding back due to a faulty pressure regulator. my recommendation is to buy a fuel pressure gauge and monitor pressure overnight. you could also pull the fuel rail and see if an injector is leaking at the same time. you can spray the intake system with a highly volitile liquid(with engine running) to see if idle speed changes to check for an air leak