Oracle DB refresh on 11g using 10g Cold backup
Datapump command like impdp can be used for importing the 10g DB contents into the 11g DB.

Update:

The above datapump command is an example of logical backup which can be done when a database is in running mode.
Below are the common steps followed during a logical backup and restore:


Export(Backup) of full DB is taken in old server:

expdp system/password@db10g full=Y directory=DIRECTORY_ON_SERVER dumpfile=DUMPFILE_NAME.dmp logfile=LOGFILE_NAME.log
Dumpfile moved to new server
Import(Restore) dumpfile in the new server:

impdp system/password@db11g full=Y directory=DIRECTORY_ON_SERVER dumpfile=DUMPFILE_NAME.dmp logfile=LOGFILE_NAME.log



  More details on this can be found in -->
  https://oracle-base.com/articles/10g/oracle-data-pump-10g (Better than
  Oracle docs)


Now coming back to the actual question, what you are asking is a restore of the cold backup in 11g DB server.

The restore of the cold backup can be done by using RMAN command(s) as below:

RMAN&gt; restore database from TAG='COLD_BACKUP_FILE_NAME'


I assume that you have taken backup of all the necessary files during the cold backup process.

Hope this helps you !!
Please share your progress with regard to this :)