Clean your windshield, inside and out,
Five minutes on a road that gets salted in the winter, and the windshield will be covered in a thin crust left behind by the brine spray from other vehicles. End result is that things will be just as bad when the sun hits you straight on.
Polarized glasses, as you mention, do help, as well as putting down the visor so you don’t stare directly into the sun.
Bold of you to assume that they’ll read past the cover.