Originally Posted by JemyM
I thought it would be easy to find a free software that simply mirrors some folders on a nightly schedule, but failed.

How's your German, JemyM?
There is a really neat tool called DirSync that I'm using myself to keep the backup folder of my secondary HDD and that of my external HDD, well, … in sync. No English version unfortunately but you should be able to figure it out even with rudimentary German skills. It's very easy to use. You create a sync job and just pick a source and a target and set some parameters and that's it.
If that doesn't work out for you then google for "rsync" and/or check out a program called DeltaCopy.

Good luck!