Hair care is an essential daily activity for many people, yet it remains inaccessible to individuals with limited mobility and challenging for autonomous robot systems due to the fine-grained physical structure and complex dynamics of hair. In this work, we present DYMO-Hair, a model-based robot hair care system. We introduce a novel dynamics learning approach suited for volumetric quantities such as hair, built on an action-conditioned latent state editing mechanism coupled with a compact 3D latent space of diverse hairstyles. This latent space is pre-trained at scale using a novel hair physics simulator, enabling generalization to previously unseen hairstyles. Using the dynamics model with a Model Predictive Path Integral (MPPI) planner, DYMO-Hair performs multimodal goal-conditioned hair styling, supporting both visual references and natural language instructions as user input. Experiments in simulation demonstrate that DYMO-Hair’s dynamics model outperforms baselines at capturing local deformation for diverse, unseen hairstyles. DYMO-Hair further outperforms baselines in closed-loop visual and language goal-conditioned hair styling tasks on unseen hairstyles, evaluated through quantitative metrics and a user study, respectively. Real-world experiments exhibit zero-shot transferability of DYMO-Hair to physical wigs, achieving consistent success across unseen wigs with varying colors, lengths, and textures. Together, these results build toward a foundation for model-based robot hair care with multi-modal goal conditioning, advancing toward more generalizable, flexible, and accessible robot hair styling in unconstrained physical environments.