The question is whether or not you see it in the Quick Styles Gallery, and if so, where. By default, Body Text is set to only show up after use, to have a recommendation priority of 100 (last), and to not display in the Quick Styles Gallery. You can change those settings using the dialog JimP pointed you to.
First, once you have changed the setting so it is displayed all the time, you need also change the priority. In the screenshot below, I changed it from 100 to 1. The screenshot is in error in that it should also have the button for all new documents based on this template clicked.
Then once that is implemented, right-click on the style in the Styles Pane to modify it (add it to Quick Styles). Check the box to add it to the quick styles and click on the button for all new documents based on this template.
Note that Styles are document and template-specific, not application-wide. That is, the styles you see in a particular document are set in that document and based on that document's template.
Understanding Styles in Microsoft Word
Templates in Microsoft Word
Images below:
- Default Quick Styles Gallery - Word 2010
- Manage Styles Dialog showing Body Text as hidden until used (alphabetical order)
- Modify Style choice when right-clicking Body Text in Styles Pane
- Modify Style dialog showing addition to Quick Styles and to template
- Quick Styles Gallery after change