And the solution:
Copy all the icons (right-click on each) and copy them firstly to your
home directory to back them up; and then copy them into the
/home/Desktop directory. After this look on the systray, bottom
righthand side and you will see (most likely, unless with you have
already messed with it) a green ball with a lower case "i" in it. This
is the new SuSEwatch thingie introduced in SuSE v8.2. Right click on it
and QUIT it. Doing so will wipe off the desktop the icons it originally
created but because you have copied them to /home/Desktop they are not
lost. After this you the icons will behave as they did in v8.1 et alia.
(There is a bug in this SuSEwatch thingie which is causing the problem
with the icons.)
BTW, when you copy the icons into the /home/Desktop directory you will
end up with 2 copies of them on your desktop until you quit/delete the
SuSEwatch button on the systray after which you will have a single copy
to play with.