Fresh installation of Ubuntu MATE 15.10 and there are no desktop icons at all. I had them the last time I installed.
This sounds like either:
-
You had the default Desktop icons on. You can check at:
System -> Preferences -> Look and Feel -> MATE Tweak
and look at the Desktop pane. You can check or uncheck various icons for the desktop
or -
You had Caja drawing icons on the desktop. This is configurable in dconf Editor (Here be dragons. dconf Editor is powerful so be careful). Go to:
Applications -> System Tools -> dconf Editor
and go to
org -> mate -> desktop -> background
and see if
show-desktop-icons
is checked?
Try toggling the option to see if icons come back or not.