It doesn't work because it sends also Shift, perceived as Shift+WheelRight or Shift+WheelLeft
@Polisson
your comment made me figure out the following fix :-

; Shift + Wheel for horizontal scrolling
+WheelDown::Send {WheelRight}
+WheelUp::Send {WheelLeft}

tested and working on windows 10

Hi all,

In case some people are still not able to fix, this seems to work for me.
I am currently using Windows 10, AutoHotkey_2.0.18

#Requires AutoHotkey v2

LShift & WheelDown:: {
    Send("{WheelRight}")
}

LShift & WheelUp:: {
    Send("{WheelLeft}")
}

Hi all,

In case some people are still not able to fix, this seems to work for me. I am currently using Windows 10, AutoHotkey_2.0.18

#Requires AutoHotkey v2

LShift & WheelDown:: {
    Send("{WheelRight}")
}

LShift & WheelUp:: {
    Send("{WheelLeft}")
}

works like a charm. Thank you

Hi all,

In case some people are still not able to fix, this seems to work for me. I am currently using Windows 10, AutoHotkey_2.0.18

#Requires AutoHotkey v2

LShift & WheelDown:: {
    Send("{WheelRight}")
}

LShift & WheelUp:: {
    Send("{WheelLeft}")
}

This works for me too. Thanks.

Works well, thanks. For anyone who wants to scope it to a specific app which may be helpful if you have other mouse-related shortcuts for other specific apps and you don't want those to conflict...also because most Windows apps already do this out of the box, just for some reason there are certain ones that don't such as OneNote...we can use something like the following. Note this is AHK v2 script, not v1.

#HotIf WinActive("ahk_exe ONENOTE.EXE")
    +WheelUp::SendInput "{WheelLeft}"
    +WheelDown::SendInput "{WheelRight}"
#HotIf