This worked for me with MSIE. I like colorful icons.- shortcuts.
At first I just dragged the IE icon just to the left of the address bar when I was at a site to my desktop. It had the site's name underneath it. But then I noticed that if I put such a site in Favorites, the icon was often pretty and colorful. Then I tried dragging these shortcuts from the favorites list to my desktop and they appeared as such. And if I had big E icons already there, they automatically changed into the colorful variation as soon as I put them in Favorites. They still have the site's name.