We investigate the physical characteristics of the Solar System's proposed Planet Nine using modeling tools with a heritage in studying Uranus and Neptune. For a range of plausible masses and interior structures, we find upper limits on the intrinsic Teff, from ~35-50 K for masses of 5-20 M_Earth, and we also explore lower Teff values. Possible planetary radii could readily span from 3 to 6 R_Earth depending on the mass fraction of any H/He envelope. Given its cold temperature, the planet encounters significant methane condensation, which dramatically alters the atmosphere away from simple Neptune-like expectations. We find the atmosphere is strongly depleted in molecular absorption at visible wavelengths, suggesting a Rayleigh scattering atmosphere with a high geometric albedo approaching 0.75. We highlight two diagnostics for the atmosphere's temperature structure, the first being the value of the methane mixing ratio above the methane cloud. The second is the wavelength at which cloud scattering can be seen, which yields the cloud-top pressure. Surface reflection may be seen if the atmosphere is thin. Due to collision-induced opacity of H2 in the infrared, the planet would be extremely blue (instead of red) in the shortest wavelength WISE colors if methane is depleted, and would, in some cases, exist on the verge of detectability by WISE. For a range of models, thermal fluxes from ~3-5 microns are ~20 orders of magnitude larger than blackbody expectations. We report a search of the AllWISE Source Catalog for Planet Nine, but find no detection.