We use the Spitzer Space Telescope to search for infrared excess at 24, 70, and 160um due to debris disks around a sample of 45 FGK-type members of the Hyades. We supplement our observations with archival 24 and 70um Spitzer data of an additional 22 FGK-type and 11 A-type Hyades members in order to provide robust statistics on the incidence of debris disks at 625Myr of age, an era corresponding to the late heavy bombardment in the solar system. We find that none of the 67 FGK-type stars in our sample show evidence for a debris disk, while 2 out of the 11 A-type stars do. This difference in debris disk detection rate is likely to be due to a sensitivity bias in favor of early-type stars. The fractional disk luminosity, L_dust_/L_*_, of the disks around the two A-type stars is ~4x10^-5^, a level that is below the sensitivity of our observations toward the FGK-type stars. However, our sensitivity limits for FGK-type stars are able to exclude, at the 2{sigma} level, frequencies higher than 12% and 5% of disks with L_dust_/L_*_>1x10^-4^ and L_dust_/L_*_>5x10^-4^, respectively. We also use our sensitivity limits and debris disk models to constrain the maximum mass of dust, as a function of distance from the stars, that could remain undetected around our targets.