As you can see, the example doesn't need a lot of changes to use sessions instead of cookies. Please notice that session values are tied to an instance of your browser. If you close down the browser, the saved value(s) will usually be "lost".
Also, if the webserver recycles the aspnet_wp.exe process, sessions are lost, since they are saved in memory as well. This can be avoided by saving session states on a separate StateServer or by saving to a SQL server, but that's beyond the scope of this article.