Excess fuel comes out as black smoke (partially burnt), or if the car doesn't start it may come out as white - just don't smoke near the fog.
When the exhaust cools down it allows cooler, moister air to enter through the tailpipe. When you start the car in the morning that moisture is heated and blown out as steam. It normally only last a few seconds, unless the evening temperature dropped significantly. If the white smoke continues for more than a minute or two, take a whiff and see if it smells sweet or acrid, that could be the sign of anti-freeze burning - not a good thing.