We present near- and mid-infrared photometry and spectroscopy from PAIRITEL, IRTF, and Spitzer of a metallicity-unbiased sample of 117 cool, hydrogen-atmosphere white dwarfs from the Palomar- Green survey and find five with excess radiation in the infrared, translating to a 4.3$_-1.2$$^+2.2$ % frequency of debris disks. This is slightly higher than, but consistent with the results of previous surveys. Using an initial-final mass relation, we apply this result to the progenitor stars of our sample and conclude that 1-7M$_☉$ stars have at least a 4.3% chance of hosting planets; an indirect probe of the intermediate-mass regime eluding conventional exoplanetary detection methods. Alternatively, we interpret this result as a limit on accretion timescales as a fraction of white dwarf cooling ages; white dwarfs accrete debris from several generations of disks for ̃10Myr. The average total mass accreted by these stars ranges from that of 200km asteroids to Ceres- sized objects, indicating that white dwarfs accrete moons and dwarf planets as well as Solar System asteroid analogues.