Non-local thermodynamic equilibrium (NLTE) effects in diagnostically important solar Fe i lines are important because of the strong sensitivity of Fe i to ionizing UV radiation, which may lead to a considerable underpopulation of the Fe i levels in the solar atmosphere and, therefore, to a sizeable weakening of Fe i lines. These NLTE effects may be intensified or weakened by horizontal radiative transfer (RT) in a three-dimensionally (3D) structured atmosphere. We analyze the influence of horizontal RT on commonly used Fe i lines in a snapshot of a 3D radiation magneto-hydrodynamic (MHD) simulation of a plage region. NLTE and horizontal RT effects occur with considerable strength (up to 50% in line depth or equivalent width) in the analyzed snapshot. Because they may have either sign, and both signs occur with approximately the same frequency and strength, the net effects are small when considering spatially averaged quantities. The situation in the plage atmosphere turns out to be rather complex. Horizontal transfer leads to line weakening relative to 1D NLTE transfer near the boundaries of kG magnetic elements. Around the centers of these elements, however, we find line strengthening, which is often significant. This behavior contrasts with what is expected from previous 3D RT computations in idealized flux-tube models, which only display line weakening. The origin of this unexpected behavior lies in the fact that magnetic elements are surrounded by dense and relatively cool downflowing gas, which forms the walls of the magnetic elements. The continuum in these dense walls is often formed in colder gas than in the central part of the magnetic elements. Consequently, the central parts of the magnetic element experience a subaverage UV-irradiation leading to the observed 3D NLTE line strengthening.