So I used to be a car mechanic for Lexus and have since changed careers, but this noise makes no sense to me. So when the car is cold and it’s cold outside, it makes a loud engine noise when under load. Things that make it worse:

-more load
-suspension load (when going over bumps at the bottom of the bump)
-colder the weather the louder the noise
-unrelated to vehicle speed, matches with engine speed

car:
2010 base sedan
108,000 miles
automatic
bone stock

Any guesses? It sounds to me almost like exhaust noise but not really.

 

Possible exhaust leak in the exhaust manifold area that closes up as parts heat up and expand.