If you've overfilled your engine with a quart too much of engine oil then yes that could be a cause of the white smoke from the exhaust.
The oil can churn in the oil pan and cause loss of lubrication as well which could cause damage to your engine so if you overfilled the engine with a quart too much oil you need to drain the excess oil down.
However the most common cause of white smoke coming from a cars exhaust is coolant being burned in the cylinders or cylinder due to a bad head gasket or warped engine head.
If it's cold outside and the white smoke is really thin then it could be just simple condensation and nothing to be worried about.
As the exhaust that is hot hits the cold air it results in water droplets known as condensation which cause the tailpipe to look like it's smoking.
If the white smoke happens in both cold and warm weather and it's thicker white smoke then it's something with the engine that needs fixed.
The thick white smoke from your exhaust usually indicates that the engine is burning coolant so check your coolant to be sure you have coolant.
The issue could be a blown head gasket, damaged or warped cylinder head, cracked engine block.
If the cause is a slight head gasket leak allowing coolant into the cylinder you can use some head gasket sealer in a bottle and mix it with warm water, drain down the coolant and run straight water in it while the head gasket sealer works.
Then be sure to flush the water out and the extra head gasket sealer and fill the radiator with coolant again to prevent it from freezing.