We report on a study of the first sample of wide binaries whose members are primarily in the old component of the Galactic disk. The binaries were discovered in 446 fields imaged with the Hubble Space Telescope (HST) Planetary Camera to an average magnitude limit of V = 2.13, as part of the Snapshot Survey for gravitational lenses. Most of the fields are at moderate to high Galactic latitude. Their total area is 0.15 deg squared. Because of the relatively faint magnitude limit, the observations are sensitive primarily to binaries in the old disk with heights above the Galactic plane of 500-1500 pc, absolute magnitudes of M(sub v) = 6-11, and physical separations of 130-4000 AU. By contrast, most previous surveys have been sensitive to binaries composed of earlier-type stars lying closer to the plane, that is, to a younger population. We find that 4% of the disk stars in the Snapshot sample have fainter companions within 1.5 mag, and separations in the range 0.13 sec is less than theta which is less than 4.0 sec. The distribution of angular separations can be fitted to a power law F(theta) is proportional to theta(exp -l), where l = 1.2 +/- 0.4, in agreement with most previous studies. The binaries in the Snapshot sample have bluer colors than would be expected for random pairs of field stars.