Only a small number of exoplanets has been identified in stellar cluster environments. We initiated a high angular resolution direct imaging search using the Hubble Space Telescope (HST) and its NICMOS instrument for self-luminous giant planets in orbit around seven white dwarfs in the 625 Myr old nearby (≈45 pc) Hyades cluster. The observations were obtained with NIC1 in the F110W and F160W filters, and encompass two HST roll angles to facilitate angular differential imaging. The difference images were searched for companion candidates, and radially averaged contrast curves were computed. Though we achieve the lowest mass detection limits yet for angular separations ≥0.5″, no planetary mass companion to any of the seven white dwarfs, whose initial main sequence masses were >2.8 M⊙, was found. Comparison with evolutionary models yields detection limits of ≈5 to 7 Jupiter masses according to one model, and between 9 and ≈12 MJup according to another model, at physical separations corresponding to initial semimajor axis of ≥5 to 8 A.U. (i.e., before the mass loss events associated with the red and asymptotic giant branch phase of the host star). The study provides further evidence that initially dense cluster environments, which included O- and B-type stars, might not be highly conducive to the formation of massive circumstellar disks, and their transformation into giant planets (with m≥6 MJupiter and a≥6 A.U.). This is in agreement with radial velocity surveys for exoplanets around G- and K-type giants, which did not find any planets around stars more massive than ≈3 M⊙.