One of the most welcome benefits of storm windows is the reduction and perhaps elimination of condensation on the interior of the existing window. Any water or ice build up is certain to cause damage to walls, sills, and to the windows themselves.
It is important to remember that "windows do not make water." They merely recognize that there is an excess of moisture inside the home or building. This excess humidity will condense on the coolest surface, which in winter is the windows. This situation is compounded by a positive pressure from a forced air furnace that steers that moisture toward leaking existing windows. It is normal to see more condensation on upper floors, because warmer air, which holds more moisture, is pushed up by cooler air, which is heavier.
Condensation on the inside face of an exterior storm window is not unusual in the Spring and Fall when the outside air is humid, and there are cool nights. You will also see moisture on your car parked outside in the morning.
Storm windows, or secondary glazing, provide insulation for cold windows, and also reduce the air infiltration through the existing windows.