I would argue that it depends on where you live. I don't think there is a simple answer there. Plus, you could have pollen, pollutants, or other unpleasantness outside of that window you have open. Perhaps you should assure that your bed and pillow are correct for you and go from there. The right pillow can make all the difference. You shouldn't be propped up too high but check with a professional (chiropractor, massage therapist, other body specialist) for the one that is right for you.

Also, check the quality of the air INSIDE the room. It's a good idea to get fresh air in the room in any case. Some people leave their windows closed all the time, switching from AC to heat, and they forget that pollutants exist in plenty of household items, such as carpets and plastics.