Preface
This is my first attempt at a Filter, be gentle.
Project Description
I am trying to finalize a build for a SSO
First, the most basic question (kind of an "is this plugged in" question), I assume that your cookies are all rooted in the same domain, and that you're not trying to get cross domain behavior here. Because cookies won't do that.
Beyond the cookie test, this looks fine. But it all hinges on the cookie test.
If you want to test the Authorization header, then you can simply short circuit the cookie test (i.e. it always passes) and populate the Authorization header with some valid value. This will, in the short term, test your whole Authorization scheme.
Once that's done/fixed, then you can focus on the cookie setting and delivery.
I also assume that you're not using Java EE Container based authentication, with Tomcat doing this check for you. In that case, a filter is simply "too late". The container will have already made it's decisions before your filter even gets called.
If you are using container based authentication, and your apps are on the same container, I would imagine Tomcat (or someone) has an SSO option at the container level. I know that Glassfish will do this for you out of the box. It should be straightforward to modify Tomcat artifacts (i.e. not portable Java EE/Servlet mechanisms) to implement this if that is the case.