Just found this guide: http://www.wpexplorer.com/custom-wordpress-welcome-message/
It explains how to create a custom plugin which will show up as a dashboard widget for the start page. It works, it shows up fine.
But there are two issues. Every widget that was there before I activated the plugin will disappear (even though they are selected in the screen options).
And if I close the Welcome-widget I created, the other widgets will not show up either. So it disables everything else.
Anyone have a better solution?
Read more here:: Custom Welcome-message removes everything else?