If the person is wearing the hat, your question would be more natural with "Did" instead of "Does".
Does the following sentence sound natural?
Does somebody make you put on that terrible hat?
If I were a native speaker of English, I would never shut up. :-)
***** NOT A TEACHER *****
James: May I be frank (very honest)?
Mona: Of course.
James: The hat that you have been wearing to work every day for the last week is very ugly.
Mona (crying): It's not my idea!
James: Does somebody make you put on that terrible hat every day?
Mona: In fact, yes. My boyfriend bought it, and he insists that I wear it every day to work.