Can dishwasher soap be used on windscreens too?

When scuba diving, we would always either spit in our goggles, or give them an extra wash with dishwasher soap to prevent them from fogging up. Could doing the same to the inside of my car's windscreen before a long road trip in freezing weather also help to prevent the buildup of fog? Sure, a defroster is good most of the time, but in super-cold weather it can't quite get rid of the fog near the top, and being a tall person I tend to like that space. And yes, I know it's not quite a diving question, but I figured my fellow divers would now best. :)