If you have a good cold backup restored you don't need to "recover" the database. Just start it up.

I think your missing the conceptual difference between a "cold backup" and a "hot backup". Your original post indicated that you took a cold backup of a database that was in archive log mode.

Just because the DB is in archivelog mode doesnt mean you can't do a cold backup and a restore of that cold backup. No need to re-create the control file using a script. Just restore the files to the original location and start the DB.