If it's a shortcut icon that appears for all users then it is normally held in the "C:\Documents and Settings, All Users, Desktop" folder and any change made to it will affect all users. This is done so that you only need one icon to serve all users, even users you may create in the future. If you want to change this behaviour you will need to copy the icon into the desktop folder for each individual user that needs it and then delete it from the All Users folder. After doing this any changes made by any user will only affect the icon for that user. It does, however, make for an untidy setup and if you uninstall a program you will need to delete all the shortcut icons for that program manually.