Nearly all outlining is primarily text-based. Some outliners provide ways of setting and controlling styles in both the header and paragraph text. The style can be reassigned automatically as the entry changes position in the hierarchy.
Word’s outliner (above) handles this, albeit awkwardly because headers must be named and styled in a particularly rigid way. But otherwise, it handles named styles as a word processor, except header character styles do not change as the header levels do. OmniOutliner has rule-based paragraph but not character styles for headers—each level of header can have a style (which carries over to columns), but notes inexplicably cannot. Inspiration has similar capabilities and control over the font for notes. Schedule and NoteBook control similar header-specific paragraph styles.