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For non-archive system's cold backups you do want the log files - when restoring you copy data, control and log files and startup, that's all.
I do not understand why are you emphasizing the difference between archivelog and noarchivelog systems as regarding to cold backup. There is absolutely no difference between the two when performing cold backup. Yo only need to backup data files and controlfiles, that's all. You don't need to backup redo logs (=online redologs) in either of the configurations.