(My first name is Gonzalo, last name Díaz).
Yes!
The "session" you can get from the request is an http Session (javax.servlet.http.HTTPSession), nothing to do with a Hibernate session (org.hibernate.Session).
And you cannot reuse the same Hibernate session all across your application. On the contrary, you should obtain the current Hibernate Session via SessionFactory.getCurrentSession(false) in your Java UI code.
The creation/reuse of these Hibernate sessions that you obtain with this method, is something Hibernate itself doesn't manage, so that is why you need a "managed environment" (such as Spring) in order to "pool" those sessions adequately.
In an article of mine here:
http://hibernar.org/articulos_en/spring ... xample.php
I explain in detail a minimal Spring+Hibernate setup, that you can use as a guideline.