In the context of exploring the possibility of using Al-powder Selective Laser Melting to fabricate horn antennas for astronomical applications at millimeter wavelengths, we describe the design, the fabrication, the mechanical characterization, and the electromagnetic performance of additive manufactured horn antennas for the W-band. Our aim, in particular, is to evaluate the performance impact of two basic kinds of surface post-processing (manual grinding and sand-blasting) to deal with the well-known issue of high surface roughness in 3D printed devices. We performed comparative tests of co-polar and cross-polar angular response across the whole W-band, assuming a commercially available rectangular horn antenna as a reference. Based on gain and directivity measurements of the manufactured samples, we find decibel-level detectable deviations from the behavior of the reference horn antenna, and marginal evidence of performance degradation at the top edge of the W-band. We conclude that both kinds of post-processing allow achieving good performance for the W-band, but the higher reliability and uniformity of the sand-blasting post-process encourage exploring similar techniques for further development of aluminum devices at these frequencies.