My '93 Accord usually handles these deep freeze winters well.  But for the
last few (very cold) days, the temperature gauge hardly rises even after a
long period of driving.  When I am at a stop and the car is idling at low
engine speed, the temp gauge sometimes rises slightly.  But when I take off
and accelerate again, it falls back to its lowest point.

Is it safe to assume that the thermostat is the culprit here?  I am guessing
that the thermostat the car has now is the original (I've had the car for
only 5 years and have not had it replaced since I've owned it).  It is also
taking longer than usual to warm up on the inside.

Am I assuming correctly?