I finally found how to do it -- in Horde, go to Mail, then Options, then Addressbooks. It might not even be visible unless you scroll down.

On the lower left, select the address book to be updated -- the default seems to be "none".

While you are at it, selct the same address book and move it to the right panel so it will be searched automatically. I think you want to select the fields at this time as well.

Save.

Now when you view a message, you get little address book icons beside each email address, allowing you to add these to the address books with a click of the icon.

Now -- how can I set this behavior to be the default for new accounts? (That has GOT to be easier than explaining all this to users!)

Bill