Personalized dialogue requires more than recalling explicit user histories: systems also need to infer hidden user states that evolve through interaction and shape appropriate response strategies. Existing memory- and profile-based methods primarily reuse observable user information, offering limited support for modeling user-state dynamics or selecting actions based on how they shape future user states. We propose PUMA (Prospective User-state Modeling for Action selection), a framework grounded in the Free Energy Principle (FEP) that formulates personalization as decision-making under partial observability, centered on an explicit user state model that captures latent user states and their action-conditioned dynamics. At each turn, PUMA maintains a belief over the user's hidden state, refines the user state model for observation generation and action-conditioned state transition, and selects dialogue actions by minimizing expected free energy, balancing epistemic and pragmatic objectives under a unified criterion. This formulation shifts personalization from passive memory retrieval to model-based decision-making over user evolution. We instantiate PUMA on healthcare-oriented counseling and motivational interviewing benchmarks with latent state annotations for rigorous evaluation. Experiments show that PUMA improves long-horizon dialogue outcomes while maintaining strong response quality, and a cross-dataset study demonstrates more reliable user-state estimation and next-state prediction.