Under the Format menu, choose "Wrap to Page" (or hit Shift Command W). This puts the current document into a page-oriented view, which adds a horizontal scrollbar and a zoom control.
Choose the menu item again (which now reads "Wrap to Window") to get rid of the zoom gadget and horizontal scrollbar.
[Editor's note: Although we don't generally publish "use this menu item to enable this feature" type of hints, I do occasionally make exceptions for things people may have overlooked ... as in this case, as I had no idea you could do this in TextEdit!]
Mac OS X Hints
http://hints.macworld.com/article.php?story=20021111055831641