By now I know it is old stuff to think mother winter's walking stick = the blackstaff. But I was thinking there might be an additional ramification to that idea.
We believe the blackstaff removes the taint of black magic from mortal casters who use it when casting black magic, protecting the caster from going nuts. But that is what it does for most wizards. If it truly belongs to Mother Winter, than I started wondering about how it might interact with the winter mantle if the wizard carrying it were the winter knight. Just thinking that might unlock a nice synergy to develop additional (unanticipated by most wizards) power for Harry in the future if he ever acquires the staff.
Then I started wondering what kind of debt mother winter might incur if he were to bring it back to her, or whether it would be his duty to return it as the winter knight.