Unlike antineutron, an antineutrino aren't made up of antiquarks so how do we tell an antineutrino from ordinary neutrino? Can majorana particle oscillates between matter particle and antiparticle?
Neutrinos might be their own antiparticles. (If we ever observe neutrinoless double beta decay, we'll know this is true.) Currently it is believed they probably aren't, in which case the oscillation you describe would be expected to be impossible as it would violate lepton number conservation.