I do something similar that you want to do.
I have a SAMBA/LDAP Domain and my windows and linux machines work ok.
The "ONE" Password with Zimbra its very easy to setup, you just need to configure zimbra to lookup the authentication in an external LDAP server, in the admin manual and in the forums are a lot of info about this.
The problem i had, was the user want the ability to change the password from zimbra, so i build this zimlet
http://wiki.zimbra.com/index.php?title=Samba_Password