Icons can be easily installed by copying them to the directory
The function Tools -> Open user directory takes you to the "freeplane_userdir". Create the directory icons if necessary and copy your own icons to it.
Restart Freeplane if necessary: you can now use your own icons in your maps.
If one of your own icons has the same filename than a standard Freeplane icon, this standard icon will be overridden. This is perfectly safe. Just remember it if you share your map with another Freeplane user, he or she will see the standard icons, not yours.
You can find the standard icons filenames in this folder of the Freeplane sources (this link lead to the 1.8.x version of Freeplane, but you can change this with the "branch" button).
Here's a preview of the icons and their filenames for Freeplane 1.8.x: