  Terrestrial planets orbiting within the habitable zones of M-stars are likely
to become tidally locked in a 1:1 spin:orbit configuration and are prime
targets for future characterization efforts. An issue of importance for the
potential habitability of terrestrial planets is whether they could experience
snowball events (periods of global glaciation). Previous work using an
intermediate complexity atmospheric Global Climate Model (GCM) with no ocean
heat transport suggested that tidally locked planets would smoothly transition
to a snowball, in contrast with Earth, which has bifurcations and hysteresis in
climate state associated with global glaciation. In this paper, we use a
coupled ocean-atmosphere GCM (ROCKE-3D) to model tidally locked planets with no
continents. We chose this configuration in order to consider a case that we
expect to have high ocean heat transport. We show that including ocean heat
transport does not reintroduce the snowball bifurcation. An implication of this
result is that a tidally locked planet in the habitable zone is unlikely to be
found in a snowball state for a geologically significant period of time.
