Archive log mode is required for hot backups; however, hot backups are not required for databases running in Archivelog mode. You can still perform cold backups with a database running in Archivelog mode. These are not mutually exclusive.
When you restore datafiles from your backup (cold or hot), try not to restore the control files if at all possible. The control files contain the most current SCN along with information about the archived redo logs. This information can make rolling forward (the recovery process) much easier.
I would highly recommend looking at Oracle Backup & Recovery Handbook by Velpuri & Adkoli on Oracle Press. It has many recovery scenarios for you to practice such as the one above.
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