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 (WDs) from the Palomar-Green survey and find five with excess radiation in the infrared, translating to a 4.3$^+2.7$ $_- 1.2$% 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 1-7 M $_☉$ 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 WD cooling ages; WDs accrete debris from several generations of disks for åisebox-0.5ex 10 Myr. The average total mass accreted by these stars ranges from that of 200 km asteroids to Ceres-sized objects, indicating that WDs accrete moons and dwarf planets as well as solar system asteroid analogs.