The official tray icon for Steam looks good with Ubuntu’s Ambiance theme, however, it doesn’t adjust its color when you change to the Radiance theme.
Luckily, in order to change the icon, all you have to do is replace the existing icon: /usr/share/pixmaps/steam_tray_mono.png
The icon is a 48 x 48 png image, so I suggest you use the same. Originally I tried modifying the colors of the official icon, however, it didn’t seem to look good with the new coloring once it was shrunk down to size.
Instead, I took an alternate icon from another article and modified the color of that one. (Note that the instructions in that article are out-of-date.)
Just save one of these images onto your computer as custom_icon.png, then browse to that folder in the command line. Once you’re in that folder, run the commands below. The last two commands set the permissions and ownership of the file to match the other files in the pixmaps folder. The icon should change within a few seconds of copying it in.
sudo mv ./custom_icon.png /usr/share/pixmaps/steam_tray_mono.png
sudo chmod 644 /usr/share/pixmaps/steam_tray_mono.png
sudo chown root:root /usr/share/pixmaps/steam_tray_mono.png