Hello,
You can browse to "Horde >> Preferences >> Mail >> Deleting and Moving Messages" to enable the following option:
"Move deleted messages to your Trash mailbox instead of marking them as deleted in the current mailbox?"
Deleting an email in Horde will automatically move the message to the "Trash" folder once you enable this option. Note that previous messages you deleted will need to be moved to the Trash folder, or "deleted" again, if you want to see those messages removed from the inbox.
Thank you.