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.
Code:
su
touch /var/log/horde.log
chown hordeuser.hordegroup /var/log/horde.log
Where
hordeuser is the user trying to create the file, and
hordegroup is the group
hordeuser belongs to.
Can't creat file in /var/log
