I'm in Wisconsin, where they throw a pound of salt on an ounce of snow! The slop that creates is far more hazardous to drive on than packed snow, an it's what causes that white film on the windshield that makes it hard to see as well.
To give you a proper answer, one thing that might help is "winter blades". There might be some other name for them, but they have thin rubber sheets along their length, one on each side of the blade, between the rubber blade and the metal frame. Those are supposed to prevent ice from forming under the frame. That ice would prevent the frame from flexing as it goes across different curves on the windshield. I've never used them myself, and I've seen many of them that had those rubber strips torn up, so I don't know how effective they are.
Some brands of washer fluid leave an oily residue that leaves streaks behind, so you might try a different brand. Nothing works as well as plain old water, but of course that will freeze once the salt has been removed. If you're using your washer fluid straight out of the jug, try mixing it with some water first.
There also used to be special cloths you could buy to clean the wiper blades. A tar-like substance builds up on them, and that will cause streaking too, even with washer fluid. Those cloths had a chemical in them to dissolve that sticky stuff and leave clean fresh rubber to squeegee the gunk off the glass.
Starting with '96 models, the Dodge Caravan had an electrically-heated lower portion of the windshield identical to what has been used for a long time on rear windows. That is to warm the area where the wiper blades park. I would be surprised if your vehicle doesn't have that feature too. You'd see the grid lines if it's there. Turn on your rear defogger to heat the windshield. They should be tied together.
Friday, February 6th, 2015 AT 10:54 AM