I would need someone to correct me on this but I believe ZorinOS's taskbar is based on the Dash To Panel gnome shell extension. It seems there's an option in the original extension to apply some padding to the icons, but unfortunately there doesn't seem to be such an option on ZorinOS. Maybe that's a feature we can request for the upcoming versions?
Based on this, I found a very hacky way to do what you're after. It's definitely not the most straight forward or ideal solution so proceed at your own risk. To be clear this works on ZorinOS Core only, it would be great if you could update your profile to reflect which version you are using.
That said, it's quite simple to do. Run the following commands on a terminal window:
// Navigate to the extension's directory
cd /usr/share/gnome-shell/extensions/zorin-taskbar@zorinos.com
// Make a backup file
sudo cp taskbar.js taskbar.js.bak
// Open the file for editing
sudo nano taskbar.js
Scroll down a bit until you see the line that says "APPICON_PADDING" and change the number to something else.
Save your changes to the file (if you are using nano that would be Ctrl + X and then press enter at the prompt).
You can use any other text editor you like, just don't use a document editor like Libre Office. You will also need elevated privileges so maybe checkout this thread if you need help with this:
Then you can press Alt + F2 which will bring up a little box where you simply type r and hit enter. This will reload your shell.
If you chose 16 like I did you will be left with some hilariously small icons:
From here it's just a matter of rinse and repeat until you find the right size for you. Note that this does not affect the main ZorinOS start menu icon, the activities overview icon or the tray system icons.
