The permission being denied is that of the /var/log directory.
The best way to solve this problem depends on the setup (I don't know anything about horde), but creating a file (as root) called /var/log/horde.log, and then chown-ing it to the appropriate user should fix it.
chown hordeuser.hordegroup /var/log/horde.log
is the user trying to create the file, and hordegroup
is the group hordeuser