Magnetic field-induced reversal of surface spin polarization for the magnetoelectric antiferromagnet chromia is studied via magnetometry in (0001)-textured thin films of various thicknesses. Reversal solely by magnetic means has been experimentally evidenced in sufficiently thin films. It sets the field-response of chromia films apart from bulk behavior, where switching between time-reversed single domain states requires the simultaneous presence of electric and magnetic fields. In our detailed experiments, we furthermore observe a giant sensitivity of the coercive field on temperature, thus, indicating the potential of magnetoelectric antiferromagnets as promising candidates for energy assisted magnetic recording media