We present new near-infrared photometry for seven late-type T dwarfs and nine Y-type dwarfs, and lower limit magnitudes for a tenth Y dwarf, obtained at Gemini Observatory. We also present a reanalysis of H-band imaging data from the Keck Observatory Archive, for an eleventh Y dwarf. These data are combined with earlier MKO-system photometry, Spitzer and WISE mid-infrared photometry, and available trigonometric parallaxes, to create a sample of late-type brown dwarfs which includes ten T9-T9.5 dwarfs or dwarf systems, and sixteen Y dwarfs. We compare the data to our models which include updated H_2 and NH_3 opacity, as well as low-temperature condensate clouds. The models qualitatively reproduce the trends seen in the observed colors, however there are discrepancies of around a factor of two in flux for the Y0-Y1 dwarfs, with T_eff~350-400K. At T_eff~400K, the problems could be addressed by significantly reducing the NH_3 absorption, for example by halving the abundance of NH_3 possibly by vertical mixing. At T_eff~350K, the discrepancy may be resolved by incorporating thick water clouds. The onset of these clouds might occur over a narrow range in T_eff, as indicated by the observed small change in 5um flux over a large change in J-W2 color. Of the known Y dwarfs, the reddest in J-W2 are WISEP J182831.08+265037.8 and WISE J085510.83-071442.5. We interpret the former as a pair of identical 300-350K dwarfs, and the latter as a 250K dwarf. If these objects are ~3 Gyrs old, their masses are ~10 and ~5 Jupiter-masses respectively.
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