Misfiring when cold?

I have a 1.2 carb engine. Im pretty sure the head gasket is going, because it uses about 2litres of water a day, white smokes, overheats and runs like crap. Would this head gasket issue cause the engine to misfire when it is cold? Starting it up in the mornings it distinctly misfires and runs on 3 cylinders for about 10 minutes, then all of a suddeen starts running fine. Also, if the car has not been running for a while, when i start it it misfires for a couple of seconds then runs fine. Had all new plugs leads dizzy cap rotor arm etc about a month a go and double checked all the ignition side of things. The engine is not staying in for much longer but im just curious as to what would cause this