Only conventional left-handed neutrinos are ruled out as significant HDM.

It is rarely mentioned amongst all the Higgs back-slapping, that the Standard Model does not yet have a complete and verified theory of neutrino physics: masses? Majorana/Dirac? self-anti-particle? chiralities? ...

There may be right-handed neutrinos that do not interact via the weak force (which is maximally parity-violating). They would only interact gravitationally and play a role dark matter:

https://en.wikipedia.org/wiki/Sterile_neutrino