i don't use desktop icons. after installation i go to menu, settings, settings-panel, files.... and deselect "show desktop icons".
i usually got nautilus and pcmanfm installed (and nautilus only cause it comes with gnome-core).
Ah, ok. Now i understand your question.
You mean icons on menu entries, not on desktop (i was confused by your example, referring the menu usual to Debian, i don't have an editors section, i forget that...)
Icons are set by .desktop files that are at folder /usr/share/applications/
To change the icons you can edit desktop file (with a text editor) but that 's not a good way, since an update can put things back again.
A better way it's copy the desktop file to ~/.local/share/applications/ and edit the new file.
It's a permanent change that overpass the defaults global one on /usr/share/... It's also, of course, a per-user change.
HTH
PS btw if you want to launch nautilus without bring the gnome desktop run it: nautilus --no-desktop