Dropdown menu widget automatically generates pages and categories menus. While generating page menu, it uses Page Order specified on Add New Page screen.
Unfortunately, for categories, this feature is not available. However you can still order your category items, using Menus under Appearance.
To achieve this, simply add a custom menu, and add all categories to your menu. Sort menu items as you like them to be.
I hope this helps you about creating your own menus.