OK, I've reskinned the FLV player component before, but I've never had to reskin the tree component. So I'm not sure what would be involved. However, I do know that most, if not all of the components that ship with the various versions of flash are fully skinnable and customisable...So reskinning and customising the Tree component should be possible.
A quick google reveals that the answer to your question most likely lies in the Adobe flash livedocs.....( http://tinyurl.com/qnxf8g - click the link and follow the top result!)
The docs state that the tree component uses an instance of the RectBorder class for its border and a scrollbar component...I'm not sure if the scrollbar is a sub-component used in the Tree's RectBorder instance, or if it is just a direct subcomponent of the Tree (like the RectBorder instance). I guess you'll have to look into that yourself!
Anyway from the link provided, you should be able to access all the help you need. Skinning of components has been around since at least mx2004, so the whole process of skinning should be well documented.
From a cursory look in the livedocs, they detail how to skin components and their sub-components, so you should be able to find all of the info you're looking for in there!
The process will probably be quite long-winded, and probably also prone to problems but I'm sure you'll get there in the end!