I’m wondering if the fields referenced here can be utilized within a custom hosted login page.
Our use case is to make minor customizations to the hosted login pages that users see based on the information available in the context object and/or client_metadata.
If it’s something that is possible, it would be very useful, as would a simple example to get started 
The context object you mentioned is only available within rules. In relation to client metadata that is also something that is not available at this time, but I’ve seen it requested a few times so it seems something much more likely to happen in the future, however, at this time there is no indication if that will indeed become available. In general, the idea/theory of the centralized login approach would be to have the same experience no matter the client application, however, the reality sometimes imposes some conflicting needs. Can you update the question with more information about the customization, would they be just user interface related?