We present a new detailed abundance study of field red horizontal branch (RHB) and blue horizontal branch (BHB) non-variable stars. High resolution and high S/N echelle spectra of 11 RHB and 12 BHB were obtained with the McDonald 2.7 m telescope, and the RHB sample was augmented by reanalysis of spectra of 25 stars from a recent survey. We derived stellar atmospheric parameters based on spectroscopic constraints, and computed relative abundance ratios for 24 species of 19 elements. The species include Si II and Ca II, which have not been previously studied in RHB and BHB (Teff < 9000 K) stars. The abundance ratios are generally consistent with those of similar-metallicity field stars in different evolutionary stages. We estimated the masses of the RHB and BHB stars by comparing their Teff--log g positions with HB model evolutionary tracks. The mass distribution suggests that our program stars possess masses of ~0.5 Msun. Finally, we compared the temperature distributions of field RHB and BHB stars with field RR Lyraes in the metallicity range -0.8 >~ [Fe/H] >~ -2.5. This yielded effective temperatures estimates of 5900K and 7400 K for the red and blue edges of the RR Lyrae instability strip.