  We study the low-temperature heat transport of HoMnO_3 single crystals to
probe the magnetic structures and their transitions induced by magnetic field.
It is found that the low-T thermal conductivity (\kappa) shows very strong
magnetic-field dependence, with the strongest suppression of nearly 90% and the
biggest increase of 20 times of \kappa compared to its zero-field value. In
particular, some ``dip"-like features show up in \kappa(H) isotherms for field
along both the ab plane and the c axis. These behaviors are found to shed new
light on the complex H-T phase diagram and the field-induced re-orientations of
Mn^{3+} and Ho^{3+} spin structures. The results also demonstrate a significant
spin-phonon coupling in this multiferroic compound.
