You can use the Application.setUserAgentStylesheet("/path/to/css") method to apply CSS files to all Scenes in your application simultaneously.
This method is also used by JavaFX itself to apply default CSS. You can always return to default CSS by calling Application.setUserAgentStylesheet(null);.
Currently, there are the following global style sheets by default, accessible by the predefined constants:
Application.setUserAgentStylesheet(STYLESHEET_CASPIAN); // JavaFX 2 and older default styleApplication.setUserAgentStylesheet(STYLESHEET_MODENA); // default style since JavaFX 8