Techniques for supporting glacier tiering of archived data in cloud/object storage are provided. In one set of embodiments, a computer system can identify one or more snapshots of a data set archived in the cloud/object storage that are scheduled to be migrated from a standard tier of the cloud/object storage to a glacier tier of the cloud/object storage. The computer system can further determine one or more data objects of the one or more snapshots that are referred to by at least one child snapshot and clone the one or more data objects in the standard tier.