F250 whistling from the rear when cold

I have a 1990 F250 4x4. Whenever its below freezing outside, I get this whistling sound coming from the rear of the truck at very low speeds, like when I’m slowing down to stop at a light, or when I’m turning a corner. Pressing either the break or gas pedal seems to make no immediate difference in the sound. I took it to my mechanic, but it wasn’t cold enough that day for him to hear it. But he did say that it is probably just that the rear differential needs servicing. Okay, so I drained and replaced the differential oil and gasket myself the next weekend. Next cold day came around and the whistling is still there. Now what?

To clarify, it’s a whistle sound that gets lower in pitch. Kind of like what you imagine an airplane sounds like when it’s landing.