Can you have "ferromagnetic" order that preserves time-reversal symmetry?

Usually in systems with ferromagnetic order, the spin $mathrm{O}(3) = mathrm{SO}(3) times Z_2^t$ (where $Z_2^t$ represents time-reversal) symmetry is broken down to $mathrm{SO}(2)$. Is it possible to have a spontaneous symmetry breaking phase where the residual symmetry group is $mathrm{SO}(2) times Z_2^t$ instead, that is, time-reversal symmetry is preserved? Is there a name for such a phase?

Note: I am not referring to spin-nematic order. In that case, the residual symmetry is $(mathrm{SO}(2) rtimes Z_2) times Z_2^t$.