My wife E60 has fuel smell at the exhaust in morning

[minilexus]

I was told that due to cold weather, the AFR rich the fuel during cold-start in the morning so you can smell petrol fume smell in the exhaust.

It is quite "Cold" in singapore lately, is the above claim true?

Or is there a leak somewhere, it is only coming from the exhaust. I cannot smell anything inside the car.

I read that is why they wrote in the manual that we should always drive off immediately after starting the car.