Vertical vs. horizontal scrolling on a mobile device

Hi All--
I've tried searching the lists, but haven't found anything addressing this question.
When is horizontal scrolling more accessible than vertical scrolling on a mobile device? Always? Never? Sometimes?
For example, envision a vertically arrayed set of categories.  Touching each category heading causes an accordion to open, displaying a subset of items. 
Is it better to have the subset appear horizontally, requiring horizontal swiping or touching, or is it better to have the subset appear vertically, requiring vertical swiping?
I know that horizontal scrolling on a desktop is to be avoided, but horizontal scrolling seems to be, from a design standpoint, acceptable on a mobile device, to limit the length of page.
What if the number of subitems arrayed vertically is quite long; is it permissible to have scrolling within the array?
Any thoughts would be greatly appreciated!
Thanks,
Mike