Currently popular models for progenitors of gamma-ray bursts (GRBs) are the mergers of compact objects and the explosions of massive stars. These two cases have distinctive environments for GRBs: compact object mergers occur in the interstellar medium (ISM) and the explosions of massive stars occur in the preburst stellar wind. We here discuss neutrino afterglows from reverse shocks as a result of the interaction of relativistic fireballs with their surrounding wind matter. After comparing with the analytical result of Waxman & Bahcall for the homogeneous ISM case, we find that the differential spectrum of neutrinos with energy from similar to3 x 10(15) to similar to3 x 10(17) eV in the wind case is softer by 1 power of the energy than in the ISM case. Furthermore, the expected flux of upward moving muons produced by neutrino interactions below a detector on the surface of the Earth in the wind case is similar to5 events yr(-1) km(-2), which is about 1 order of magnitude larger than in the ISM case. In addition, these properties are independent of whether the fireballs are isotropic or beamed. Therefore, neutrino afterglows, if detected, may provide a way of distinguishing between GRB progenitor models based on the differential spectra of neutrinos and their event rates in a detector.