Print Manager Does not Show Printers

It sounds like the Forest Trust is using Selective Authentication. If so, you need to grant DomainB users the "Allowed to Authenticate" permission on the print server computer object in ADUC in DomainA.

Although what you're trying to accomplish isn't technically just the migration of all printers from a 2003 box to a 2012 box, it is a part of it. As HelplessN00b mentioned the way to migrate is quite simple actually and requires you to add the Print and Documentation Role to your Server 2012 machine. However I'd offer that what you are doing is more of a fresh restart on a new 2012 box with the newest drivers and settings configured and then applying them to all printers; things like B&W and duplex settings. To accomplish this add the Print role to your 2012 server as described in my instructions below:

Server Manager > Add Roles and Features > click through and then select Print and Documentation Services

To actually migrate the printers from 2003 to 2012 (which you will need to do first even if you are changing settings and drivers) follow this guide which I like: http://www.urtech.ca/2013/06/solved-how-to-migrate-printers-into-server-2012/

After that, you can set the settings you want on your base/vanilla printers then export these settings and re-import them to all the rest of the printers. How you export the settings is described in detail here: http://technet.microsoft.com/en-us/library/cc722360.aspx

Although the link applies to 2008, it will work for 2012.