Improving the sealing of windows and doors to reduce the air leaks will improve the efficiency of your heating and cooling but it also increases your risks of dampness because there isn't air ...
Running a dehumidifier will help. Also bringing in fresh air to your heating unit is essential to having the correct air pressure. As the furnace runs it will draw the fresh air it needs. Contact a heating a cooling installer, they should be able to help out.
Furnaces, unless they are the new high efficiency type, don't need fresh air. Air yes, fresh no.
AND, the only reason high efficiency furnaces use fresh air is to eliminate the necessity of using heated air to go out the exhaust.
Kitepflyer, you are correct, that is why I recommended contacting a heating and cooling contractor. Maybe the doors and windows aren't the only thing lacking efficiency?