We present optical spectroscopy and near-infrared photometry of 126 cool white dwarfs (WDs) in the Sloan Digital Sky Survey (SDSS DR3). Our sample includes high proper motion targets selected using the SDSS and USNO-B astrometry and a dozen previously known ultracool WD candidates. Our optical spectroscopic observations demonstrate that a clean selection of large samples of cool WDs in the SDSS (and the SkyMapper, Pan-STARRS, and the Large Synoptic Survey Telescope data sets) is possible using a reduced proper motion diagram and a tangential velocity cut-off (depending on the proper motion accuracy) of 30km/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 WD 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 8Gyr. A few ultracool WDs may be as old as 12-13Gyr, but our models have problems matching the spectral energy distributions of these objects. There are only two halo WD candidates in our sample. However, trigonometric parallax observations are required for accurate mass and age determinations and to confirm their membership in the halo.