Is there an API way to go back and time and list all the hosts that were part of a particular asset group from 12-01-2018 to 12-31-2018?
I don't think there's a way to get the point-in-time configuration of an asset group.
But you could use the Activity Log to backtrack and see what changes have been made.
Go to Users > Activity Log, filter the logs and you should see these changes:
Retrieving data ...