It has been shown that F, G, and early K dwarf hosts of Neptune-sized planets are not preferentially metal-rich. However, it is less clear whether the same holds for late K and M dwarf planet hosts. We report metallicities of Kepler targets and candidate transiting planet hosts with effective temperatures below 4500K. We use new metallicity calibrations to determine [Fe/H] from visible and near-infrared spectra. We find that the metallicity distribution of late K and M dwarfs monitored by Kepler is consistent with that of the solar neighborhood. Further, we show that hosts of Earth- to Neptune-sized planets have metallicities consistent with those lacking detected planets and rule out a previously claimed 0.2dex offset between the two distributions at 6{sigma} confidence. We also demonstrate that the metallicities of late K and M dwarfs hosting multiple detected planets are consistent with those lacking detected planets. Our results indicate that multiple terrestrial and Neptune-sized planets can form around late K and M dwarfs with metallicities as low as 0.25 solar. The presence of Neptune-sized planets orbiting such low-metallicity M dwarfs suggests that accreting planets collect most or all of the solids from the disk and that the potential cores of giant planets can readily form around M dwarfs. The paucity of giant planets around M dwarfs compared to solar-type stars must be due to relatively rapid disk evaporation or a slower rate of planet accretion, rather than insufficient solids to form a core.