You don't use a Character Style for this; you use a Paragraph Style. Which in this case would be named 'footnote' or 'Footnote' and be applied to all of the actual footnotes in the document. Changes to the Footnote style will then be applied to all paragraphs tagged Footnote.
Just in case that's not (quite) the issue, you can't select multiple footnotes at a time. Each is in a layout 'bubble' of its own. The only way to manage the styles is to make sure footnotes are assigned that consistent paragraph style, and adjust that style.
This is a very basic layout, design and InDesign concept, and if you don't grasp Paragraph Styles you may wish to work though a few basic tutorials on how to use the fundamentals of ID's layout features.