Last night, after the students night cross country flight, we approached our home field after the tower closed and made the usual position reports on CTAF (which is the tower frequency) . After departing the runway we advised traffic that we were clear of the runway and on taxiway "X" and proceeding to a specified parking area. This was all done on the tower frequency, which reverts to CTAF when the tower is closed.
The airfield we are based at has a taxiway that leads into the parking area. To my suprise just before turning on to the taxiway I noticed an aircraft on that taxiway. We stopped and avoided a nose to nose situation.
Now the question. We were on CTAF which I believe is correct. Should we have switched to the ground frequency while taxiing even though the tower and ground control have gone home for the night.