The oil warning light indicates no oil pressure to the engine. Continuing to drive a car in this condition can result in serious engine damage. The vehicle smokes just for about 10-15 seconds after starting then goes away. This happens only when cold. The plugs are clean and are burning even, no oil on them.
Warm starts are fine.
We have found similar problems with other cars with approximately 60,000 or more miles. Replacing the valve stem seals reduces the oil use. I waited a little while and went further when I noticed white smoke coming from the exhaust. It is still registering full. I thought it was a head gasket.