Prerequisites

1. Enable the multilib repository by editing /etc/pacman.conf
2. Install WineHQ and some other optional dependencies:

   $ pacman -Syu wine
   $ pacman -S --asdeps lib32-mpg123 lib32-gnutls {lib32-,}gst-plugins-base-libs \
                        lib32-alsa-plugins lib32-libpulse lib32-openal
   $ yay -S lib32-unixodbc # or your favourite AUR helper

3. We'll install a 64-bit version of iTunes, so no need to set WINEARCH

What iTunes version

Version 12.8 seems to work fine. I had troubles making more recent >=12.9 versions work (see here). Same for older versions (e.g. 12.5), I could not log in to the Apple Store. So find yourself the (64-bit) iTunes64Setup12.8.exe installer somewhere on the internet.

Install and Run

Just

$ wine /path/to/iTunes64Setup12.8.exe

And go through the procedure. Start iTunes with

$ wine .wine/drive_c/Program\ Files/iTunes/iTunes.exe

Issues

1. No playback: solved with

   Preferences > Playback > Play Audio Using > Direct Sound
   

2. CD-ROM detection: to make Wine aware of your CD-ROM unit:

   $ mkdir /mnt/cdrom
   $ ln -s /mnt/cdrom ~/.wine/dosdevices/z:
   $ echo '/dev/sr0 /mnt/cdrom iso9660 defaults,user,noauto 0 0' > /etc/fstab
   $ systemctl reboot

   Check if the /dev/sr0 device really represents your CD-ROM unit. The CD pops up in iTunes only if the CD is inserted before starting the program.