Is there any way to change what cores SQL 2012 Enterprise uses? Suppose you have 16 cores on a server, what is the process of going through and telling the database to only actively use 2 cores? Is that even possible?
Yes, it's doable via Affinity Masking, or by virtualizing the SQL server and only provide the number of vCpu's that you have licensed.
I'm guessing that you have 8 licenses when you need 16, per the new SQL 2012 licensing scheme. We can't help you with licensing issues here, you'll have to ask your Microsoft representative if masking complies with the licensing rules.