While the engine is cold, different things happen in the motor.
First, it's not at operating temperature so tolerances are looser. The turbo will be cold, its bearings not up to temp, so spooling it up too much might not help its longevity.
Second, the glow plugs are probably still operating and the fuel rail pressure might be a little higher than normal.
Third, the EGR should be closed for the entire time.
Fourth, the clutch on the cooling fan would not be engaged as it is coolant-temperature-dependent.
These factors will influence how the engine sounds.
I wonder if you've got a boost leak when the engine is cold, because the metal interfaces haven't expanded to their normal operating position? Perhaps in EGR valve area?