Techniques for tiering data to a cold storage tier of a cloud object storage platform are provided. In one set of embodiments, a computer system can identify one or more old snapshots of a data set that reside in a first storage tier of the cloud object storage platform, where the one or more old snapshots are snapshots that are unlikely to be deleted from the cloud object storage platform within a period of N days. The computer system can further, for each snapshot in the one or more old snapshots: identify one or more data blocks in the snapshot that are superseded by a more recent snapshot in the one or more old snapshots; write the one or more data blocks to a second (i.e., cold) storage tier of the cloud object storage platform that has a lower storage cost than the first storage tier; and cause the one or more data blocks to be deleted from the first storage tier.