Supernova (SN) cosmology without spectroscopic confirmation is an exciting new frontier, which we address here with the Bayesian Estimation Applied to Multiple Species (BEAMS) algorithm and the full three years of data from the Sloan Digital Sky Survey II Supernova Survey (SDSS-II SN). BEAMS is a Bayesian framework for using data from multiple species in statistical inference when one has the probability that each data point belongs to a given species, corresponding in this context to different types of SNe with their probabilities derived from their multi-band light curves. We run the BEAMS algorithm on both Gaussian and more realistic SNANA simulations with of order 104 SNe, testing the algorithm against various pitfalls one might expect in the new and somewhat uncharted territory of photometric SN cosmology. We compare the performance of BEAMS to that of both mock spectroscopic surveys and photometric samples that have been cut using typical selection criteria. The latter typically either are biased due to contamination or have significantly larger contours in the cosmological parameters due to small data sets. We then apply BEAMS to the 792 SDSS-II photometric SNe with host spectroscopic redshifts. In this case, BEAMS reduces the area of the Ω m , ΩΛ contours by a factor of three relative to the case where only spectroscopically confirmed data are used (297 SNe). In the case of flatness, the constraints obtained on the matter density applying BEAMS to the photometric SDSS-II data are ΩBEAMS m = 0.194 ± 0.07. This illustrates the potential power of BEAMS for future large photometric SN surveys such as Large Synoptic Survey Telescope.