I recently upgraded to Windows 10 and JavaFX code which worked in Windows 8.1 appears to freeze up in 10. I\'ve tracked the issue down to opening a ComboBox within a dialog.
As mentioned in other answers, this is likely an error to do with Intel graphics processors and it appears not to be solved by a driver update.
However, while this bug is hopefully being fixed, for now I recommend adding an event which focuses the combobox upon a mouse press and therefore solves the problem. Simply add the code below:
comboBox.setOnMousePressed(new EventHandler(){
    @Override
    public void handle(MouseEvent event) {
        comboBox.requestFocus();
    }
});