P.S. Another thing to check for cold starting problems is an "internal fuel system leak". That is a "fuel damper" or "fuel accumulator" or check valve leak in the fuel system.

Normally the fuel system will retain pressure with the car off. But if there is an "internal leak", then there is no fuel pressure when you go to start the car, thus poor cold starting.

Here is an example of a service manual write-up for testing that - (maybe not for your specific car, be sure to get the factory service manual for your specific car).

07.3-120 - Testing fuel pressures and internal leakage...
http://www.benzworld.org/forums/attachments/w126-s-se-sec-sel-sd/1597065d1441366173-hello-orange-county-ca-fuel-pressure-gasser-126-073-120.pdf