After you've typed the text, switch to the pointer tool and then click on the down arrow of the Font Family selector. Use the down arrow of the keyboard to scroll the font list. Press Enter to select one.
Are you using the Mac version? When I use the arrow keys it shows a little preview popup, but it doesn't effect the real text until I select one.
That's correct. It does not affect the text until you select one. There's no feature in Fireworks that enables you to scroll the font list and have the text updated live.
You could submit a feature request to Adobe regarding this issue: https://www.adobe.com/cfusion/mmform/index.cfm?name=wishform
Also, some font managers—like Suitcase Fusion or Linotype FontExplorer—allow you to preview fonts in the form of a see-through overlay feature, which might be useful for you.
You might also be interested in developer Aaron Beall's Font Panel—which at this point is purely a concept, not an actual extension. I don't know if Aaron's actively developing this panel or not, but you could email him and let him know the functionality you're looking for. It might be something he could integrate into the panel, if and when it gets developed.