Hydrodynamics captures the slow dynamics of thermal systems, and in holography these modes are encoded in black-hole geometries. The hydrodynamic fields can be viewed as keeping track of the relative coordinate frame between the asymptotic boundary and the horizon. Rather than integrating out these degrees of freedom, one keeps them explicit and solves only the bulk dynamics of the remaining fields. This leads to a partially on-shell description in which the bulk constraints associated with conservation are left unsolved and reappear as equations of motion of the effective theory. Doing so requires specifying appropriate infrared data at the horizon. We show that the horizon symplectic structure provides a natural way to organize these boundary conditions and gives a covariant interpretation of the mixed conditions used in recent holographic constructions. This perspective also clarifies their relation to horizon symmetries and quantum chaos.