Currently the Presets system handles only the numerical parameters (it uses a ini file to store the values). Obviously, this method is very limited because
Forest keeps multiple external references that must be transferred to scene: custom objects, surfaces, materials, areas, etc.
We are working in a new Presets method, integrated with the library browser. In this way, would be possible to store full Forest objects with all their elements. Hopefully, it will be ready for the next update.
The easiest mode to copy a Forest object from other scene is to use Import->Merge, but selecting all referenced objects. For this, turn on "Display Influences" and "Select Influences" in the merge dialog. Once imported, just assign the new areas and surfaces.
To copy a Forest object within a same scene, just use Clone (Ctrl+V) and select "Copy". That should work fine.