This is a nice idea, however I would rather see daily Bible verses than random fortunes. Here is how to do that. First, install the verse package:
$ sudo apt-get install verse
Then, edit /usr/bin/mint-fortune with sudo, and replace the line:
/usr/games/fortune | $command -f $cow
/usr/bin/verse | sed -e 's@^ *@@' | $command -f $cow
To be sure that the file won't be overridden when you upgrade your distribution, set it as a local diversion:
$ sudo dpkg-divert --local /usr/bin/mint-fortune
and you're done!