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The short answer is, you cannot - not with the standard Tree component. This could probably be implemented with customized Tree and VTree, but that would require client side changes.
However, you can use Tree.ItemStyleGenerator for at least partial control on how to display the items in a tree (defining CSS classes for individual items).
There is the ticket 2661 about a tree that would support Vaadin components as nodes, but it is currently not targeted to any near future version. If you want to gather support for it, you could create a suggestion about it in UserVoice.
I have also seen a contributed ComponentTree where you can create a tree of Vaadin components, but it was at an experimental stage and probably does not support the container API. I cannot find it in source code control, stay tuned for the Vaadin directory (coming soon) from which you will probably be able to download it.