Is it possible to 'hide' a page to everyone but a certain user or group of users?
Yes, you'd go into the library that contains the page and set item level permissions for the page assuming you have the permissions to do so. Or you could create it in a separate library with unique permissions.
You can make use of the Audiences feature that allows you to restrict visibility of the page via several different mechanisms, including Groups, distribution lists or other rules based on profile data.
If you have publishing turned on you can do this as well by unpublishing the pages, then you can create groups with specific permissions to see pages in various states.