We present a study of the multi-wavelength properties, from the mid-infrared to the hard X-rays, of a sample of 255 spectroscopically identified X-ray selected type-2 AGN from the XMM-COSMOS survey. Most of them are obscured and the X-ray absorbing column density is determined by either X-ray spectral analyses (for 45% of the sample), or from hardness ratios. Spectral energy distributions (SEDs) are computed for all sources in the sample. The average SEDs in the optical band are dominated by the host-galaxy light, especially at low X-ray luminosities and redshifts. There is also a trend between X-ray and mid-infrared luminosity: the AGN contribution in the infrared is higher at higher X-ray luminosities. We calculate bolometric luminosities, bolometric corrections, stellar masses and star formation rates (SFRs) for these sources using a multi-component modeling to properly disentangle the emission associated to stellar light from that due to black hole accretion. For 90% of the sample we also have the morphological classifications obtained with an upgraded version of the Zurich estimator of structural types (ZEST+). We find that on average type-2 AGN have lower bolometric corrections than type-1 AGN. Moreover, we confirm that the morphologies of AGN host-galaxies indicate that there is a preference for these type-2 AGN to be hosted in bulge-dominated galaxies with stellar masses greater than 1010 solar masses.