We have conducted spectrum analyses of 24 field metal-poor ([Fe/H]<-2) red horizontal-branch (RHB) stars identified in the HK objective-prism survey and 6 such stars in the globular cluster M15, based on high-quality spectra (R~40000, S/N~100) obtained with the Magellan Inamori Kyocera Echelle spectrograph at the Clay 6.5m telescope at Las Campanas Observatory. The atmospheric parameters of the RHB stars provide interesting bridges between turnoff stars of similar temperature and red giant branch (RGB) stars of similar gravity, and they permit investigations of abundance trends [X/Fe] versus [Fe/H] in a relatively unexplored region of the temperature-gravity plane. We find that the Teff, logg, vt, and [Fe/H] values determined from our spectra are consistent with expectations from literature spectroscopic studies of other evolved metal-poor stellar classes.