Smoke out of A/C vents
 

I started my car, turned A/C on and started driving.

About 5 minutes later, white smoke started coming out of my air vents. When I turned the A/C OFF but kept the fan on, the white smoke went away.

I turned A/C back on and white smoke came out again.

This smoke is odorless.

I tried the A/C again later in the day. The White smoke did not re-appear.

It was lightly raining when this happened. Not sure if that has anything to do with it.

It's likely fog, not smoke... Cold air mixing with hot, humid air causes the moisture to condense. Have you ever seen the white smoke that comes out of your freezer when you open it? ;)

I agree with shadrach, it has happened to mine once, same thing, wet cold morning, fired it up and a condensation type vapor, streamed out for a short time (no more than a minute) then it was fine. With yours having no odour it sounds more like the cold air vapour, just the atmospheric condition at the time.

You will obviously keep an eye on it anyway, but hopefully all should be good.

It could also be the heater core. It would have a bit of antifreeze smell, but that's a classic sign of impending heater core failure. If you let it go too long, you'll have a nice lake of antifreeze on you passenger floor.