Ok, here is what worked for me.

Select Format, then Styles and Formatting, go to the Show dropdown menu and choose ?Custom?, then click Styles, highlight footnote reference, choose modify, format, font, check Superscript, then check Ok, (here you can check the ?add to template? to add it to the Normal.dot), then click Ok, and then click Apply.

That changed the footnote style for the entire document, including new footnotes.

However, one thing I don't understand is what is a "Style" format and how do you use it and how do you delete it from Normal.dot. Somehow, I now have a "Style Footnote Reference" which makes the footnote red (came from the doc that Dreamboat saved above). I can delete it in any document, but can't figure out how to delete it in Normal.dot. Also, I'd like to know what the hell that's used for.