I would like to create custom styling for the label in a field for a table in a view. Is this possible within the view edit page? Or will I have to define a custom CSS class and write the styling in the css pages included in the theme?
CSS in the theme (or in the module that provides the View) is the best way to do this.
Yes, it is possible within the view edit page.
You just need to click on the field.
Then under Styles Settings, check mark Customize label HTML. Select DIV or SPAN as element, then type a class name.