Difficulty breathing through nose at night? Should I give up my feather pillow?

Possibly, +. It is certainly possible that your nasal passages are reacting to environment at night, such as pillow, down blanket, dusty carpet, mites or other dust particles floating around. It could also be that air is too dry. In fact probably most people mouth breath at night, wake up with very dry mouth, and stuffy nose. So, can try correcting this and that, and see what happens. Try saline nasal spray.