Why is exhaust smoky on cold start?

no info generic answer if lucky most likely blew a head gasket worst cracked block --white exhaust smoke is steam your burning water/coolant

White smoke indicates water going through your engine or condensation in your exhaust. If it is a lot of smoke you probably have a small leak in your head gasket that seals back up as the engine warms and the materials expand. It will get worse as time goes on. If it's just a little smoke that doesn't last long it's probably condensation in your exhaust, especially if it's cold outside. Condensation is caused by the air cooling down in your exhaust after you shut down the engine.

Hi, you do not give a great deal of info about your car, but I will assume that it has done50K miles and is 5 years old.
All combustion engines produce CO2 and Water as part of the Carbon cycle, to produce energy. The same as when you breath out.
When the car is cold ("at start up") this water will show as steam in the exhaust fumes until the exhaust pipe has heated up, the water vapour is then not visible.
Also residual fuel in the exhaust gas will be expelled as the engine usually adds extra fuel to make starting easier at low temperature. On a modern engine the air intake has a heater to preheat the air to assist this process. Excess fuel in the exhaust gas may be coloured Black.
Faults in the cylinder head gasket may allow cooling system water to enter the cylinder bore under cooling system pressure after a journey. When the car is restarted from cold this water will be expelled into the exhaust system, and would be visible as white smoke ( steam) in the exhaust gas at start up. If the cooling system is being topped up on a regular basis, with no other leaks evident, this should be suspected, the smell of antifreeze from the cooling system being detected in this exhaust gas would be a further clue.

Never buy a car without seeing it start from cold, running it till hot and checking for the above. It can be 'disguised' by unscrupulous dealers selling a 'trade in' car through the trade. As on some fairly basic cars the cost is well in excess of £1000.00 (Yes) and count yourself lucky at that. Many other faults can cause smoke at start up, usually engine needs a major service . rebuild.

rings might be going bad but try an additive for that exhaust smoke first through the motor

What happening is you have a bad head gasket or its starting to go bad. As long a little oil is getting in to cylinders causing that smoke once it warms up that gasket is expanding thus the smoke stops. I would keep an eye on oil levels if it gets milky replace gasket asap. Could also be intake gasket but highly doubt it this sounds like a worn head gasket.

Try changing the Air Filter and Diesel Filter, Also add diesel injector cleaner into the diesel filter housing and the remains to the tank.

Hope this helps

White smoke is caused by engine coolant / antifreeze being processed in the combustion chamber(s) of the engine

Keep in mind that, on a cold day you may see what appears to be white smoke from the exhaust that will disappear after the vehicles engine has warmed up to it's normal operating temp.. This is a normal reaction called condensation... condensation is the result of a small amount of water/dew being drawn into the exhaust usually collecting in the muffler and/or the catalytic converter.

Hope helps.

Does the engine smokes blue on cold start?
Does it runs rough at coldstart?

Then check the glowplugs / glow system.

Ouch! you've got engine coolant in the exhaust from a leak somewhere...DO NOT run this engine until you get someone (dealer is best in this instance) to diagnose ($50-125)

Could be valve guides. They are plastic sleeves through which the valve stems pulse up and down thousands of time a minute and wear, especially if the oil is crummy.
When the engine shuts off, the oil in the upper engine drips down onto the tops of the pistons and cooks off to a nice blue smoke when you start it. The valve guides are supposed to prevent this.