Answer
It would work, but there are severe shortcomings.
Work Step by Step
Headlights should have filters with horizontal axes of polarization, while windshields should have vertical axes. Thus, light from oncoming headlights will be completely extinguished. No more glare! The windshield would also reduce glare from reflections off the road.
Major shortcomings include the fact that the headlights’ output is reduced by 50 percent immediately, and that the amount of light transmitted by the windshields is also down by 50 percent, even for non-polarized sources.
It would be like wearing sunglasses at all times while driving, and the reduced visibility would be dangerous.
