Bedroom window open or shut at night if you are a hay-fever sufferer, which is better?

Shut: "Hay fever" generally applies to environmental pollen sensitivity, so I recommend shutting the windows. However, indoor allergens are more problematic this time of year (unless trees have begun to pollenate in n. CA), so opening/shutting the window may have little effect. Skin testing for allergen sensitivity can help refine successful avoidance strategies and guide therapy. See an Allergist.