When it is below freezing why would a 1996 Neon engine indicator go up to overheating after about 20 minutes on the road and blow cold air?

check the thermostat to see if it is opening properly (you can remove it and place it in a pan of water on the stove and heatthe water until it opens oh yeah don't forget to use a thermometer to find out what temp. it was) you should also check your antifreeze mixture for accurracy(try that first) if none of these work try flushing your heater core to see if it is stopped up

This could be an indication that you do not have enough antifreeze. The car heater will not work when there is no liquid in it. also the car will overheat.