Actually, this is a lie, there is one cookie if you login using one of the third party Authorisation platforms, that cookie is your session. It is validated whenever your request needs to be checked for permission for whatever it is you want to do, If that session cookie isn't there your authorisation will be asked for again. And that's all.
If you wish you can disable cookies for the site and you will be nagged pretty much whenever you do something. But nothing will break.