We consider a low-temperature plasma within a newly developed magnetohydrodynamic fluid model. In addition to the standard terms, the electron spin, quantum particle dispersion, and degeneracy effects are included. It turns out that the electron spin properties can give rise to ferromagnetic behavior in certain regimes. If additional conditions are satisfied, a homogeneous magnetized plasma can even be unstable. This happens in the low-temperature high-density regime, when the magnetic properties associated with the spin can overcome the stabilizing effects of the thermal and Fermi pressure, to cause a Jeans-like instability.