Due to deep automation, the configuration of many Cloud infrastructures is static and homogeneous, which, while easing administration, significantly decreases a potential attacker's uncertainty on a deployed Cloud-based service and hence increases the chance of the service being compromised. Moving-target defense (MTD) is a promising solution to the configuration staticity and homogeneity problem. This paper presents our findings on whether and to what extent MTD is effective in protecting a Cloud-based service with heterogeneous and dynamic attack surfaces - these attributes, which match the reality of current Cloud infrastructures, have not been investigated together in previous works on MTD in general network settings. We 1) formulate a Cloud-based service security model that incorporates Cloud-specific features such as VM migration/snapshotting and the diversity/compatibility of migration, 2) consider the accumulative effect of the attacker's intelligence on the target service's attack surface, 3) model the heterogeneity and dynamics of the service's attack surfaces, as defined by the (dynamic) probability of the service being compromised, as an S-shaped generalized logistic function, and 4) propose a probabilistic MTD service deployment strategy that exploits the dynamics and heterogeneity of attack surfaces for protecting the service against attackers. Through simulation, we identify the conditions and extent of the proposed MTD strategy's effectiveness in protecting Cloud-based services. Namely, 1) MTD is more effective when the service deployment is dense in the replacement pool and/or when the attack is strong, and 2) attack-surface heterogeneity-and-dynamics awareness helps in improving MTD's effectiveness.