We investigate the effects of horizontal radiative transfer (RT) a NLTE on important diagnostic iron lines in a realistic 3-D HD simulation. Using a multi-level atom we compute and compare widely used Fe I line profiles at 3 different levels of approximation (3-D NLTE, 1-D NLTE, LTE). We find that the influence of horizontal RT is of the same order of magnitude as that of NLTE, although spatially more localized. Also, depending on the temperature of the surroundings, horizontal RT is found to weaken or strengthen spectral lines. Line depths and equivalent width may differ by up to 20% against the corresponding LTE value if 3-D RT is applied. Residual intensity contrasts in LTE are found to be larger than those in 3-D NLTE by up to a factor of two. When compared to 1-D NLTE, we find that horizontal RT weakens the contrast by up to 30% almost independently of the angle of line of sight. While the CLV of the 1-D and 3-D NLTE contrasts are of similar form, the LTE contrast CLV shows a different run. The determination of temperatures by 1-D NLTE inversions of spatially resolved observations may produce errors of up to 200 K if one neglects 3-D RT. We find a linear correlation between the intensity difference of 1-D and 3-D NLTE and a simple estimate of the temperature in the horizontal environment of the line formation region. This correlation could be used to coarsely correct for the effects of horizontal RT in inversions done in 1-D NLTE. Horizontal RT is less important if one considers spatially averaged line profiles because local line strengthening and weakening occur with similar frequency in our HD atmosphere. Thus, the iron abundance is underestimated by 0.012 dex if calculated using 1-D NLTE RT. Since effects of horizontal RT are largest for spatially resolved quantities, the use of 3-D RT is particularly important for the interpretation of high spatial resolution observations.