  We present optical spectroscopy and near-infrared photometry of 126 cool
white dwarfs in the Sloan Digital Sky Survey (SDSS). Our sample includes high
proper motion targets selected using the SDSS and USNO-B astrometry and a dozen
previously known ultracool white dwarf candidates. Our optical spectroscopic
observations demonstrate that a clean selection of large samples of cool white
dwarfs in the SDSS (and the SkyMapper, Pan-STARRS, and the Large Synoptic
Survey Telescope datasets) is possible using a reduced proper motion diagram
and a tangential velocity cut-off (depending on the proper motion accuracy) of
30 km/s. Our near-infrared observations reveal eight new stars with significant
absorption. We use the optical and near-infrared photometry to perform a
detailed model atmosphere analysis. More than 80% of the stars in our sample
are consistent with either pure hydrogen or pure helium atmospheres. However,
the eight stars with significant infrared absorption and the majority of the
previously known ultracool white dwarf candidates are best explained with mixed
hydrogen and helium atmosphere models. The age distribution of our sample is
consistent with a Galactic disk age of 8 Gyr. A few ultracool white dwarfs may
be as old as 12-13 Gyr, but our models have problems matching the spectral
energy distributions of these objects. There are only two halo white dwarf
candidates in our sample. However, trigonometric parallax observations are
required for accurate mass and age determinations and to confirm their
membership in the halo.
