Large-scale data centers enabling today's cloud services are now hosting a tremendous amount of servers and virtual machines. To enable scalable and highly available management of such data centers, we have proposed Snooze, a novel Infrastructure-as-a-Service (IaaS) cloud management system based on a self-organizing and self-healing hierarchical architecture of system services. In this challenge, we present an extensive scalability study of Snooze across five geographically distributed clusters of the Grid'5000 experimentation testbed. Particularly, we focus on the system setup time, self-organization and self-healing protocols, system services resource consumption, and the application deployment scalability. The results indicate that the current Snooze prototype implementation is robust enough to manage thousands of servers and hundreds of VMs. Moreover, its autonomic behavior allows to achieve high availability at scale. Finally, Snooze has been successfully used to run data-intensive Hadoop MapReduce applications.