So in agreement with @justinmeyer and as a Cubase user who is now using the S1 keyboard shortcuts, the following will work.
|Ctl+Shift + MouseWheel Forward
||Zoom in horizontally|
|Ctl+Shift + Mouse Wheel Backward
||Zoom out horizontally|
|Shift + Mouse Wheel Forward
||Scroll Horizontal backward (i.e. towards the beginning)|
|Shift + Mouse Wheel Backward
||Scroll Horizontal forward (i.e. towards the end)|
And of course, Ctl + Mouse Wheel to achieve vertical zoom of tracks
Note: the interplay of Zoom Horizontal and Scroll Horizontal when you have the song completely zoomed out to appear completely in the arranger window is a bit clunky, if you try to zoom into the son again you will need to set the cursor into a section of the song to get the zoom to zoom and stay within the song itself, i.e. it doesn't start zooming past the end of the song.
Hope this helps. I don't mean in any way to suggest that the excellent use of the mouse as demonstrated in Joe Gilder's old tutorial is of less value but for people who may have difficulty with positioning the mouse with speed and accuracy and/or who come from the excellent Cubase wheel mouse scrolling this is an important feature for quickly feeling comfortable and attaining fluid speed in S1
Studio One 4 Pro