From Forum Nokia Wiki

You should use CEikEdwin::SetBackgroundColorL() to set the Edwin's background colour.

CustomEdwin.cpp

void CMyEditorContainer::ConstructL(const TRect& aRect)
{
   ...
   iEdwin = new (ELeave) CEikGlobalTextEditor;
   iEdwin->SetContainerWindowL(*this);
   iEdwin->SetBackgroundColorL(KMyCustomColor);
   ...
}

CustomEdwin.h

class CMyEditorContainer: public CCoeControl, MCoeControlObserver
{
   ...
    private:
        CEikGlobalTextEditor*   iEdwin;
   ...
}

Links

How to use custom background color for edwin in 3rd

--