We present H- and K-band spectra for late-type Kepler Objects of Interest (the "Cool KOIs"): low-mass stars with transiting-planet candidates discovered by NASA's Kepler Mission that are listed on the NASA Exoplanet Archive. We acquired spectra of 103 Cool KOIs and used the indices and calibrations of Rojas-Ayala et al. (2012, Cat. J/ApJ/748/93) to determine their spectral types, stellar effective temperatures, and metallicities, significantly augmenting previously published values. We interpolate our measured effective temperatures and metallicities onto evolutionary isochrones to determine stellar masses, radii, luminosities, and distances, assuming the stars have settled onto the main sequence. As a choice of isochrones, we use a new suite of Dartmouth predictions that reliably include mid-to-late M dwarf stars. We identify five M4V stars: KOI-961 (confirmed as Kepler 42), KOI-2704, KOI-2842, KOI-4290, and the secondary component to visual binary KOI-1725, which we call KOI-1725B. We also identify a peculiar star, KOI-3497, which has Na and Ca lines consistent with a dwarf star but CO lines consistent with a giant. Visible-wavelength adaptive optics imaging reveals two objects within a 1 arcsec diameter; however, the objects' colors are peculiar. The spectra and properties presented in this paper serve as a resource for prioritizing follow-up observations and planet validation efforts for the Cool KOIs.