I did some more troubleshooting and found the issue.

I first uninstalled MagicMirror (npm uninstall MagicMirror).
In the second step, I renamed the existing MagicMirror directory into MagicMirror_old.

Then I reinstalled it like described here, git clone, npm install-mm, copying default config etc.
After starting MM with the default config, all is fine.

I then copied over my old config.js and restarted MM --> still working fine.

But after copying my custom.css file, the icon was broken again.
After commenting out section by section, this was the section that caused the broken icon:

.light {
        font-family: "Roboto Condensed", sans-serif;
        font-size: 80px;
        line-height: 125px;
        font-weight: 300;
}

I then commented out line by line and as soon as I commented out the “font-family” line, the icon was displayed nicely again.