We present new effective temperature and surface gravity determinations for a sample of 90 hot white dwarfs detected in the Extreme Ultraviolet Explorer (EUVE) all-sky survey. The measurements, based on spectroscopy of the Balmer line series obtained at the Michigan-Dartmouth-MIT Observatory, Mount Stromlo Observatory, Lick Observatory, and Cerro Tololo Inter-American Observatory, are used to constrain the space density as well as the population age and mass distribution of a sample of 110 EUV-selected DA white dwarfs in the solar neighborhood. We find a mass spectrum narrowly peaked over 0.56 M&sun;, indicative of a C-O core with a thin hydrogen layer, and a significant population of 10 ultramassive (M >= 1.1 M&sun;) white dwarfs; we also find that all objects fall between effective temperatures of ~25,000 and ~75,000 K and that most are younger than 30 Myr. Using Wood's evolutionary models we determine a DA white dwarf birthrate in the solar neighborhood of (0.7--1.0) x 10-12 pc-3 yr-1. Although most objects are on normal C-O cooling tracks, we suggest that a few low-mass white dwarfs and the population of ultramassive white dwarfs may follow different paths with, respectively, He, and, possibly, O-Ne-Mg cores.