You won't see them in Word's File Open and Save dialogs if you have the file
type set to All Word Documents rather than All Files. I don't think you can
hide them in Windows Explorer (except perhaps by hiding Hidden and System
files, though I think that affects just the temp files).
Hey, you can hide all your backup files by searching "backup" in the search bar in your documents folder and then select all the backup files then right-click for the Properties option then check the "hidden" box. That will hide all the files and you'll never have to see their faces again!