  We report the complete photometric results from our Herschel study which is
the first comprehensive program to search for far-infrared emission from cold
dust around young brown dwarfs. We surveyed 50 fields containing 51 known or
suspected brown dwarfs and very low mass stars that have evidence of
circumstellar disks based on Spitzer photometry and/or spectroscopy. The
objects with known spectral types range from M3 to M9.5.
  Four of the candidates were subsequently identified as extragalactic objects.
Of the remaining 47 we have successfully detected 36 at 70micron and 14 at
160micron with S/N greater than 3, as well as several additional possible
detections with low S/N. The objects exhibit a range of [24]--[70] micron
colors suggesting a range in mass and/or structure of the outer disk. We
present modeling of the spectral energy distributions of the sample and discuss
trends visible in the data. Using two Monte Carlo radiative transfer codes we
investigate disk masses and geometry. We find a very wide range in modeled
total disk masses from less than 1e-6 solar masses up to 1e-3 solar masses with
a median disk mass of order 3e-5 solar masses, suggesting that the median ratio
of disk mass to central object mass may be lower than for T Tauri stars. The
disk scale heights and flaring angles, however, cover a range consistent with
those seen around T Tauri stars. The host clouds in which the young brown
dwarfs and low-mass stars are located span a range in estimated age from ~1-3
Myr to ~10 Myr and represent a variety of star-forming environments. No obvious
dependence on cloud location or age is seen in the disk properties, though the
statistical significance of this conclusion is not strong.
