High-resolution maps of polarization anisotropies of the cosmic microwave background (CMB) are in high demand, since the discovery of primordial B-modes in the polarization patterns would confirm the inflationary phase of the universe that would have taken place before the last scattering of the CMB at the recombination epoch. Transition edge sensors (TES) and microwave kinetic inductance detectors (MKID) are the predominant detector technologies of cryogenic detector array-based CMB instruments that search for primordial B-modes. We propose another type of cryogenic detector to be used for CMB survey: a magnetic microbolometer (MMB) that is based on a paramagnetic temperature sensor. It is an adaption of state-of-the-art metallic magnetic calorimeters (MMCs) that are meanwhile a key technology for high resolution α, β, γ, and x-ray spectroscopy as well as the study of neutrino mass. The effort to adapt MMCs for CMB surveys is triggered by their lack of Johnson noise associated with the detector readout, the possibility of straightforward calibration and higher dynamic range given it possesses a broad and smooth responsivity dependence with temperature, and the absence of Joule dissipation which simplifies the thermal design. A brief proof of concept case study is analyzed, taking into account typical constraints in CMB measurements and reliable microfabrication processes, to assess the suitability of metallic magnetic sensors in CMB experiments. The results show that MMBs provide a promising technology for CMB polarization survey as their sensitivity can be tuned for background limited detection of the sky while simultaneously maintaining a low time response to avoid distortion of the point-source response of the telescope. As the sensor technology and its fabrication techniques are compatible with TES-based bolometric detector arrays, a change of detector technology would even come with very low cost.