Sono riuscito a risolvere il problema con quest'istruzione:
SessionFactory sessionFactory = new Configuration().addFile("C:/percorso-completo-file/META-INF/hibernate.cfg.xml").buildSessionFactory();

Però ora Tomcat mi dice:
INFO: Initialize action of type: actions.ActionRegistrazioneControl
32 [http-8080-Processor24] INFO org.hibernate.cfg.Environment - Hibernate 3.3.1.GA
63 [http-8080-Processor24] INFO org.hibernate.cfg.Environment - hibernate.properties not found
63 [http-8080-Processor24] INFO org.hibernate.cfg.Environment - Bytecode provider name : javassist
78 [http-8080-Processor24] INFO org.hibernate.cfg.Environment - using JDK 1.4 java.sql.Timestamp handling
157 [http-8080-Processor24] INFO org.hibernate.cfg.Configuration - Reading mappings from file: C:\DOCUMENTI DANILO\Workspace\Videoteca\WebContent\META-INF\hibernate.cfg.xml
297 [http-8080-Processor24] WARN org.hibernate.connection.UserSuppliedConnectionPro vider - No connection properties specified - the user must supply JDBC connections
org.hibernate.HibernateException: Hibernate Dialect must be explicitly set