We present observations of the 6300 Å [O I] spectral region in two cool Hyades dwarfs, vB 79 and vB 25. We derive a mean iron abundance, [Fe/H]˜+0.11, in good agreement with recent analyses of F and G Hyades dwarfs. The O abundance derived from spectrum synthesis, [O/H]˜+0.15, is between the values deduced by Garcia Lopez et al. (1993, ApJ, 412, 173; [O/H]=-0.05 to -0.10) and King (1993, Ph. D. Dissertation, University of Hawaii; [O/H]=+0.26), who employed the 7774 Å O I triplet in hotter Hyades dwarfs. An accounting of differences between these two 7774 Å analyses is given. Our [O I]-based determination suggests the Hyades O abundance itself is super-solar, though [O/Fe]˜0.0; however, systematic errors as large as 0.10-0.15 dex cannot be ruled out. The Hyades giants show an unexpected ˜0.23 dex O deficit relative to our dwarf value. While some suggestive evidence for non-standard nuclear processing and mixing in the Hyades giants may exist, we find it unconvincing. Rather, model atmosphere deficiencies or [O I] -region blending features that are still unrecognized by laboratory and theoretical efforts may contribute to the giant-dwarf O discrepancy. Finally, our high O abundance is marginally consistent with values claimed to provide a solution to the Hyades Li problem from standard stellar models. However, it is not clear that these models do in fact reproduce the extant Li data. Our Li abundance upper limit for vB 25 is at least 0.5 dex lower than the abundances of two tidally locked binaries of similar Teff. Standard stellar models of uniform composition and age are not able to reproduce such scatter in Li.