Accurate extraction of cosmological parameters from upcoming weak lensing surveys relies on knowledge of the total matter power spectrum at percent level at scales k < 10 h/Mpc, for which modelling the impact of baryonic physics is crucial. In Chisari et al (2018) , we presented measurements of the total matter power spectrum from the Horizon cosmological hydrodynamical simulations: a dark matter-only run, one with full baryonic physics, and another lacking feedback from Active Galactic Nuclei (AGN). The simulations correspond to cosmological boxes of 100 Mpc/h on each side and share the same initial conditions and WMAP7 cosmology. We found a suppression of power at intermediate scales (k~10 h/Mpc) of <15% at z=0, and an enhancement of a factor of a few at smaller scales due to the more efficient cooling and star formation in the baryonic runs. The redshift evolution of the effect of baryons on the matter power spectrum is non-monotonic throughout the range z=0-5 due to an interplay between AGN feedback and gas pressure, and the growth of structure. Total matter power spectra from the Horizon simulation are made publicly available here. There are three files, each of them corresponding to a different simulation run. Hz-AGN refers to the full baryonic physics run. Hz-noAGN corresponds to the run with no AGN feedback. Hz-DM is a dark matter only run. The first row of the files indicates the quantities in each column: the first one is the wavenumber, k [h/Mpc]; the following ones are dimensionless power spectra (\Delta^2) at different redshifts, as indicated by the header. Notice that redshifts are not the same across files. If you use these results in your work, we ask that you cite Dubois et al. (2014) and Chisari et al (2018).