Here's how I finally got it work. I put it in very detailed form, so anyone can follow it easily.
1) Open terminal (Ctrl+Alt+T)
2) In terminal, run following commands:
sudo apt-get install xautomation
sudo apt-get install xbindkeys
3) Create a new file called .xbindkeysrc.scm to your home directory, by running in terminal
gedit ~/.xbindkeysrc.scm
4) Add the following text to the file, save it, and close the text editor:
; bind shift + vertical scroll to horizontal scroll events
(xbindkey '(shift "b:4") "xte 'mouseclick 6'")
(xbindkey '(shift "b:5") "xte 'mouseclick 7'")
5) In terminal, run command
xbindkeys
6) With Firefox browser, go to address about:config
7) Change following values (double click on value)
mousewheel.with_shift.action to 0 (from the default 2)
mousewheel.with_shift.action.override_x 1 to 1 (from the default -1)
8) Now Shift+Mouse Scroll should lead to horizontal scrolling on Firefox, instead of the default Back/Forward action.
Extra information:
3) .xbindkeysrc.scm is a hidden file (because it starts with a dot), and that's why you cannot see it with nautilus or other filesystem browser by default. You can hit Ctrl+H to see hidden files.
5) It seems, that you have to run it only once -- not at every time you log on. I also tried removing the xbindkeys and the horizontal scroll worked until next reboot/login.
7) If you set them as 1, -1, you will get "diagonal scroll" when trying to scroll fast. That's why I think it is necessary to use options 0, 1 instead of 1, -1.