How I can deploy Edubuntu from one machine to many machines in the same domain and authenticate to Windows Active Directory?
Why not use LTSP-Cluster and integrate the server with your AD.
LTSP is already integrated into Edubuntu as an option during installation.
PiNet "Centralised user accounts and file storage system for a Raspberry Pi classroom" might be the solution you are looking for.
I think I would use Clonzilla: http://clonezilla.org/ You have to make an image from one of your computers than restore this image to others. There is a good and useful guide on the web page.I think this is the fastes way, and you also have a clean backup image
For AD authentication you can use likewise open or Centrify Express both of them free for use. You need to add the domain name the rest will be done by the app. On the next logon you can use the domain authentication.
I hope my answer will be useful