We examine the impact of baryonic physics on the halo distribution in hydrodynamic simulations (Illustris, IllustrisTNG, and EAGLE), particularly with regards to how it differs from that in dark matter only (DMO) simulations. We find that, in general, DMO simulations produce halo mass functions (HMF) that are shifted to higher halo masses than their hydrodynamic counterparts, due to the lack of baryonic physics. However, the exact nature of this mass shift is a complex function of mass, halo definition, redshift, and larger-scale environment, and it also depends on the specifics of the baryonic physics implemented in the simulation. We present fitting formulae for the corrections one would need to apply to each DMO halo catalogue in order to reproduce the HMF found in its hydrodynamic counterpart. We provide these formulae for all three simulations, for five different halo definitions at redshifts 0, 1, and 2. Additionally, we explore the dependence on environment of this HMF discrepancy, and find that, in most cases, halos in low density environments are slightly more impacted by baryonic physics than halos in high density environments. We thus also provide environment-dependent mass correction formulae that can reproduce the conditional, as well as global, HMF. We show that our mass corrections also repair the large-scale clustering of halos, though the environment-dependent corrections are required to achieve an accuracy better than 2%. Finally, we examine the impact of baryonic physics on the halo mass - concentration relation, and find that its slope in hydrodynamic simulations is consistent with that in DMO simulations. Ultimately, we recommend that any future work relying on DMO halo catalogues incorporate our mass corrections to test the robustness of their results to baryonic effects.