  Cold, low-mass, field brown dwarfs are important for constraining the
terminus of the stellar mass function, and also for optimizing atmospheric
studies of exoplanets. In 2020 new model grids for such objects were made
available: Sonora-Bobcat and ATMO 2020. Also, new candidate cold brown dwarfs
were announced, and new spectroscopic observations at lambda ~4.8 um were
published. In this paper we present new infrared photometry for some of the
coldest brown dwarfs, and put the new data and models together to explore the
properties of these objects. We reconfirm the importance of mixing in these
atmospheres, which leads to CO and NH_3 abundances that differ by orders of
magnitude from chemical equilibrium values. We also demonstrate that the new
models retain the known factor >~3 discrepancy with observations at 2 <~ lambda
um <~ 4, for brown dwarfs cooler than 600 K. We show that the entire 1 <~
lambda um <~ 20 energy distribution of six brown dwarfs with 260 <= T_eff K <=
475 can be well reproduced, for the first time, by model atmospheres which
include dis-equilibrium chemistry as well as a photospheric temperature
gradient which deviates from the standard radiative/convective equilibrium
value. This change to the pressure-temperature profile is not unexpected for
rotating and turbulent atmospheres which are subject to diabatic processes. A
limited grid of modified-adiabat model colors is generated, and used to
estimate temperatures and metallicities for the currently known Y dwarfs. A
compilation of the photometric data used here is given in the Appendix.
