Sorry, I have no idea where the horde DB would be nor how to dump it. Is it a mysql db? Is it its own independant db?
Before I go on, which address book is empty? The system shared address book, or the individual user address books? If it's the system address book, do as ergozd has suggested, except substitute turba (address book) for kronolith (calendar). If it's the individual user address books, then you can try this. This assumes that both servers are running the same version of horde. Do from the server console:
1. On the old server, mysqldump --opt horde > /root/horde.sql <--This dumps the horde table.
2. Look through this file and verify that you can see the individual user address books.
3. Make sure you have all of the users created on the new server.
4. On the new server, mysqldump --opt horde > /root/horde_current.sql <--Dump the current horde db just in case you need to revert.
5. mysqladmin drop horde <--This drops the horde DB from mysql from the new server
6. mysqladmin create horde <- create new horde db
7. mysql horde < /root/horde.sql <--This imports the horde db from the old server to the new server.
8. login as a user that is supposed to have personal contacts and check them.
If you have issues, then repeat steps 5 - 8 but use the horde_current.sql and you should be back to where you started.
HTH,
JB