You can do this by handling the WebDropDown's DropDownOpened client event.  In the handler, you can find the ID of the WebDataTree and get an instance of the control.  Then, you can set the active node with the set_activeNode() property, passing in the root node.  You can see a code sample that I have tested with your sample below:

ASPX Markup:

<ig:WebDropDown ID="wddTree" runat="server" Width="170px" ... >
    <ClientEvents InputKeyUp="setFocus" DropDownOpened="dropDownOpenedHandler"/>

Java script:

function dropDownOpenedHandler(sender, args) {
    // Find the ID of our nested WDT.
    var id = $(sender.get_element()).find(".igdt_Control")[0].id,
        treeInstance = $IG.WebDataTree.find(id);

    // Make the root node active.
    treeInstance.set_activeNode(treeInstance.getNode(0));
}

If you have any further questions or concerns with this, let me know.