There's an option to show/hide desktop icons in Xubuntu.

https://lists.ubuntu.com/archives/xubuntu-users/2008-April/001096.html

As for installing icons I would not know how to.

however that shows how to shut off the existing OEM icons.
I'm trying to find a way to add application icons to the desktop.
When I ran XFCE through Ubuntu, I cheated by adding the icons in Gnome
and then logging back in to XFCE and having my icons. I do not have
that luxury in Xubuntu.

You're looking to add icons in...

Let me know how far you get, as I enjoy
the Xubuntu most out of the buntu series.

Well, actually i think it's a preference towards
Thunar file manager and the XFCE environment
as I run XFCE Cassandra (Mint) on my IBM desktop.

I got ticked off and installed Ubuntu.