Due to lack of space to hang onions I was going to put them in large mesh bags inside an old large wooden chest in unheated room - will they keep over winter this way or do they absolutely have to have air flowing around them?
They have to be dry. That probably does imply a degree of air circulation.
Mesh bags yes, but I'd be chary of the wooden chest. The main thing is to be able to check them regularly so you can remove any starting to rot. If I had a crop this year I'd put them in my old tights with a knot between each one....
Sadly, other problem is that I didn't read up on cropping them and most were just pulled out of the ground rather than being gently loosened so I'll be lucky if they keep very well anyway. (Chest easily accessed for checking which is why I wanted to use it but will probably store some if the loft which has greater air flow and is nice and dark).