Techniques are provided for managing snapshot volume trees in a snapshot-enabled data storage system. A snapshot management system is configured to maintain a snapshot volume tree for a storage volume of a storage system, wherein the snapshot volume tree comprises a data structure which comprises a plurality of snapshot volume nodes corresponding to respective ones of (i) a root volume and (ii) multiple snapshots related directly or indirectly to the root volume, wherein the snapshot volume nodes comprise respective generation times which denote times that the respective snapshot volume nodes were created. The generation times are used in conjunction with write times of data items that are written to the snapshot volume nodes to manage snapshot reading and deletion operations.