The basement temperature is not that cold because the soil moderates the conditions on the outside of the wall. The basement temperature has no direct effect caused by the daily air temps outdoors. You can insulate the walls if you choose. Remember there is no magical line on the wall at the theoretical frost depth because of the three dimensional flow of heat. Look at the area of the cold floor in comparison to the wall temperatures.
Regarding the "ventless" fireplace, that couls be very dangerous and ubhealthy. If it is a direct vent sealed gas fireplace with both a fresh air intake and a vent through a chimney, they have been shown to be safe.