This seems like a common use, so I suspect I'm missing something...
During my daily planning, I add or remove tasks for the day by changing the task's scheduled day (C-c s). I use column view while in the agenda view for the day to see how much I've scheduled for the day. When I complete a task, I mark it DONE.
I don't want the DONE tasks to show up in this view because their time still contributes to the total (I want a running total of what I have left in the day).
But I can't figure-out how to filter by TODO status. '/' lets me filter by tag, but how do I filter by status?
I think what you want is to set org-agenda-skip-scheduled-if-done to t.
See the Manual: Deadlines and Scheduling. It will hide any scheduled tasks that are already completed.