This is a wild guess, but if there is a 12V relay, 12V motor, or 12V pump, and it isn't getting enough voltage, then it could make that kind of noise. You mentioned that it happens when very cold. Check your 12V battery voltage when you have the problem. If it is <11V, that is almost definitely the problem.
When it's buzzing, see what happens when you jump a second battery onto the car. If it goes away, you've certainly pinpointed the problem.
Again, this is a guess, but if your battery is 2-3 years old, it's a possibility.
Bob