If everything were at zero temperature you probably* would not be able to distinguish between the past and future. Mathematically time would still exist, in the same way that spatial directions still exist on a completely featureless plane, but since it would not be measurable (even if there were something around that could do a measurement!), it is debatable whether it could be considered physically meaningful.
However, this has nothing to do with being at zero temperature itself. The world would also be time-symmetric if it were in equilibrium at a finite temperature. It is the fact that you are at equilibrium that makes time become unimportant, not at which temperature this equilibrium occurs. There is a fascinating history of theories about the relation between being out of equilibrium and time's arrow, summarized up for example in the popular account From Eternity to Here by Sean Carroll.
*It's not completely clear that this is true, actually. Google around for 'time crystals,' a proposal by Nobel Laureate Frank Wilczek. I'm not sure of the current status of this proposal.