Does everyone have an administrative account? If not, have you looked at their account settings and parental controls? Have you looked at the preferences that allow discs to be visible. This article covers the variety of preferences:
Thank you. That helps. No, I'm the only admin. I did look at their account settings and parental controls, but didn't find what I was looking for. However, your article showed me where to find the settings for removing the EHD icons from the desktop.
Unfortunately, I realized other users can still access my EHDs by using the Finder anyway. Oh well, at least with them off the desktop my kids are less likely to explore and accidentally delete my photos.
Or is there a way to make my EHD only accessible to me?