I think you simply haven't mapped the horizontal events to anything. ns-win.el contains the following:
(global-set-key [vertical-scroll-bar down-mouse-1] 'ns-handle-scroll-bar-event)
(global-unset-key [vertical-scroll-bar mouse-1])
(global-unset-key [vertical-scroll-bar drag-mouse-1])
If I do the same with `horizontal-scroll-bar' I can drag it around, and Emacs react to it. (Unfortunately, it then scroll the window vertically rather than horizontally, but that just a technicality :)
Also, if you evaluate (read-key-sequence "Click on something: ") and either click on the empty space next to the scroll bar or drag it, it will return events with the type `horizontal-scroll-bar'.
Thanks for starting to work on the NS port!