No. Both Torah scrolls and ancient Greco-Roman papyrus scrolls are written sideways, in columns of a consistent width. The rollers are held in the hands.
replyModern fantasy depictions of vertical scrolls leave an erroneous impression that the book proceeds in a downward direction, in addition to the cliché use of 'see above' to prefer to anything previously in the text. Hypertext media and text editors further support this misunderstanding by applying continuous scrolling to a document. This confusion is quite new, perhaps as recent as the 1980s.
Scrolls written in a single column and "scrolled" vertically (like a modern text editor or web browser) weren't completely unheard of, particularly for liturgical or legal documents. See http://grbs.library.duke.edu/article/viewFile/9191/4607
replyBut, yeah, the horizontal format would've been more common.