Horizon fluxes of energy and angular momentum are a key strong-field effect in the dynamics of black holes, encoding direct information about their nature. In this work, we present a numerical study of these fluxes for a test particle orbiting a Kerr black hole on equatorial geodesics, covering circular, eccentric, and hyperbolic trajectories across a wide range of orbital parameters and black hole spins. We reproduce known results for circular orbits and uncover a richer phenomenology for eccentric and hyperbolic ones: the instantaneous fluxes can exhibit multiple peaks and sign changes, indicating a complex interplay between orbital dynamics and horizon perturbation. We then compare these results against existing analytical post-Newtonian expressions, exploring resummation strategies to improve their performance against numerical data. In particular, we propose a factorized and resummed representation of the horizon fluxes that predicts the onset frequency of the superradiant regime to within $10\%$ for $\gtrsim 83\%$ for both the energy and angular momentum fluxes of bound configurations; high-energy open orbits however remain a challenge. This representation exactly reduces to the circular limit by construction, independently of the perturbative order of the remaining analytical terms. For peak and orbit-averaged fluxes, the analytical models achieve acceptable accuracy – with relative errors at the $10\%$ level or below – at large separations and low eccentricities. However, they can exhibit deviations of $\sim 𝒪(100\%)$ in the strong-field regime, motivating the need for improved flux prescriptions and further investigations.