Assuming you mean moisture on the INSIDE of the windshield.. it is very most likely a leaking heater core or some other form of coolant leak into the passenger cabin. The reason it doesn't do it when the window is cracked is because it equalizes the temp and humidity on both sides of the glass. That's just basic science. In other words, leaving the window cracked probably has nothing to do with what is involved with the moisture to happen in the first place. It is just treating the symptom and not the problem.
Frost forms on the inside of your windshield when warm, moist air inside the car comes into contact with the cold surface of the glass, causing the moisture in the air to condense and freeze. This can happen when the temperature inside the car is higher than the temperature outside.
It depends on the size of the crack. Windows cannot have any broken glass or cracks greater than 1 inch in the windshield wiper area, no cracks greater than 2 inches outside of it or any cracks longer than 3 inches that extend into this area.
Heated air is coming up the vents on the inside. If it has enough moisture, it will condense on the relatively cooler windshield. The same thing happens when there is warm moist air being circulated inside the car, and the outside air is cold.
Did you try moving the wipers arms a notch or two so when they start they are not at the bottom of the windshield but rather an inch or so above the bottom edge of the windshield to make them sweep farther to the outside?
I THE WINDSHIELD
Your car's windshield may be constantly icing up in cold weather due to a combination of factors such as humidity inside the car, outside temperature, and lack of proper ventilation. The moisture inside the car can condense on the windshield and freeze in cold temperatures, leading to ice formation. Using a defroster and ensuring proper ventilation can help prevent this issue.
To eat fish
"A bright sunrise" could rhyme with "outside" and reference a good morning.
They are usually located in the cowl----the slotted area right below the outside of the windshield.
The A/C runs to help defrost the windshield by removing moisture from the air. The fans run to help the cool off the condenser.
If you look through the windshield from OUTSIDE on the DRIVERS SIDE you will see the VIN plate near the base of the windshield on top of the dash
Lower left corner of the windshield, viewed from outside.