Magnetization and susceptibility measurements have been made on pure and ${\mathrm{Fe}}^{2+}$-doped MnC${\mathrm{O}}_{3}$ powders of \ensuremath{\sim}0.5-\ensuremath{\mu}m particle size. Through the disappearance of weak ferromagnetism, the ${\mathrm{Mn}}^{2+}$ spin system is seen to be reoriented from the basal plane to the trigonal axis as the Fe content is increased. Zn doping has no such effect. The reorientation is thought to be caused by the large uniaxial anisotropy of the ${\mathrm{Fe}}^{2+}$ ground-state spins, with the Mn spin direction being determined mainly by competition between Mn-Fe exchange and the relatively small magnetic dipolar anisotropy of Mn favoring the basal plane. The remanent weak moment decreases rapidly above a critical concentration of 0.5 at.% Fe, to about $\frac{1}{10}$ of the undoped value for 2 at.%. For higher dopings, the materials behave as uniaxial antiferromagnets at low fields, but their nonlinear susceptibility shows that spin rotation in an external field returns the Mn sublattices toward the basal plane; a critical field of \ensuremath{\sim}25 kOe is inferred from the data for 5 at.% Fe. In the transition doping range, a large thermoremanent offset moment results in shifted hysteresis loops of the normal weak moment. This offset, amounting to a maximum of \ensuremath{\sim}1.5 ${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ per ${\mathrm{Fe}}^{2+}$ ion at a doping level of 0.9 at.%, is attributed to stabilization of the ${\mathrm{Fe}}^{2+}$ polarization, induced near ${T}_{N}$, by an exchange barrier arising out of a non-collinear Mn-Fe spin arrangement. Below the critical concentration, the near absence of an offset moment implies that the Mn and Fe spins are either almost parallel or almost perpendicular to each other. By considering a simple model, the latter is taken to be the most probable situation. At the upper end of the transition range (\ensuremath{\sim}2 at.% Fe), ${\ensuremath{\chi}}_{0}(T)$ shows a weak ferromagnetic-to-antiferromagnetic transition near ${T}_{N}\ensuremath{-}1\ifmmode^\circ\else\textdegree\fi{}$K. The variation of ${T}_{N}$ with doping is nonlinear, ${T}_{N}$ being 34.5, 35, and 38 \ifmmode^\circ\else\textdegree\fi{}K for 0, 5, and 20 at.% ${\mathrm{Fe}}^{2+}$, whereas the reported value for FeC${\mathrm{O}}_{3}$ is 38.3 \ifmmode^\circ\else\textdegree\fi{}K. Also pointed out is the probability of occurrence of a photomagnetic effect, in this and similar systems, through an effective reduction in the doping concentration by excitation of the impurity ions.