We analyze theoretically a possible influence of neutrino magnetic moments on the propagation of ultrahigh-energy (UHE) cosmic neutrinos in the interstellar space. Using most stringent astrophysical bounds on the putative neutrino magnetic moment, probabilities of neutrino flavor and spin oscillations are calculated. Under the assumption of two-neutrino mixing, specific patterns of spin and flavor oscillations are determined for neutrino-energy values characteristic of, respectively, the cosmogenic neutrinos, the Greisen-Zatsepin-Kuz’min (GZK) cutoff, and well above the cutoff.