Hide is the same as remove to me. https://www.google.com/search?q=hide+icons+in+system+tray+windows+8&gl=US
If you have an app the "minimizes to the tray" then fixing that is specific to the App if you want it to exit rather that min to tray.
I'd like to remove (not hide) some icons from the Notification Area. My research indicates that it's only possible to remove icons for programs that have been uninstalled, and even that can only be done by hacking the registry. The icons I want to remove are for programs that are still installed, but don't belong there. These are programs that you close, but instead of exiting, they move themselves to the system tray, and you only know that if you click on Customize.
Windows must be storing the icon information somewhere. Is it possible to access that list and delete unwanted entries?