I have never heard it in English either, and don't think it is a common term at all, but in Norwegian it is very common usage, where hvitevarer (white goods) is fridges, washing machines, dishwashers etc, and brunevarer (brown goods) are steroes, TVs etc.

If you go some decades back, almost all steroes and TVs were brown (typically wood or brown plastic), while dishwashers and fridges were nearly always painted white.