Context. The Event Horizon Telescope recently observed the first shadow of a black hole. Images like this can potentially be used to test or constrain theories of gravity and deepen the understanding in plasma physics at event horizon scales, which requires accurate parameter estimations. Aims. In this work, we present Deep Horizon, two convolutional deep neural networks that recover the physical parameters from images of black hole shadows. We investigate the effects of a limited telescope resolution and observations at higher frequencies. Methods. We trained two convolutional deep neural networks on a large image library of simulated mock data. The first network is a Bayesian deep neural regression network and is used to recover the viewing angle i, and position angle, mass accretion rate Ṁ, electron heating prescription R_high and the black hole mass M_BH. The second network is a classification network that recovers the black hole spin a. Results. We find that with the current resolution of the Event Horizon Telescope, it is only possible to accurately recover a limited number of parameters of a static image, namely the mass and mass accretion rate. Since potential future space-based observing missions will operate at frequencies above 230 GHz, we also investigated the applicability of our network at a frequency of 690 GHz. The expected resolution of space-based missions is higher than the current resolution of the Event Horizon Telescope, and we show that Deep Horizon can accurately recover the parameters of simulated observations with a comparable resolution to such missions.