Howl from behind - Toyota Corolla, 1.6L, 2000

Due to the severe Siberian winter (from -30 and below) the bridge froze over the night. In the morning there was a strong howl, which stopped after 2-3 km.
Spring came, the howl became quieter, I generally thought it was thorns. Having changed shoes for the summer, the unpleasant sound remained.
I went to the service. They drained the oil from the bridge, uzhs, black goo with pieces of iron shavings. They filled in some kind of ravinol, like 8w80 (I can't remember). The howl became less bass, but remained.
By the way, almost nothing is heard on the passenger seat.

Conclusion - in this situation, four-wheel drive is evil.

UPDATE It's not the gearbox at all, the reason was the wheel bearing.