We consider a minimal extension of the Standard Model with a hidden sectorcharged under a dark local U(1)′ gauge group, accounting simultaneously for light neutrinomasses and the observed Dark Matter relic abundance. The model contains two copiesof right-handed neutrinos which give rise to light neutrino-masses via an extended seesawmechanism. The presence of a stable Dark-Matter candidate and a massless state naturallyarise by requiring the simplest anomaly-free particle content without introducing any extrasymmetries. We investigate the phenomenology of the hidden sector considering the U(1)′ breaking scale of the order of the electroweak scale. Confronting the thermal history of thishidden-sector model with existing and future constraints from collider, direct and indirectdetection experiments provides various possibilities of probing the model in complementaryways as every particle of the dark sector plays a specific cosmological role. Across the iden-tified viable parameter space, a large region predicts a sizable contribution to the effectiverelativistic degrees-of-freedom in the early Universe that allows to alleviate the recentlyreported tension between late and early measurements of the Hubble constant.