Windshield on a bike
Windscreens are more about rider comfort than decreasing air resistance. I would think particularly with the upright riding position of a mountain bike that your hypothetical installation of a windscreen would increase air resistance, unfortunately, by expanding the area of mass that would push against the air.

The common advice for getting more aerodynamic on a bike boils down to get low and small. This is why cyclists trying to hit speed records always duck down while gripping drop-style handlebars. They also wear tight-fitting clothes, use specially-shaped helmets, get a bike that is engineered specifically to cut through the air quite efficiently, etc.

So I'd conclude that if what you're looking for is not so much maximizing your possible speed but rather getting the wind out of your face, there's nothing inherently wrong with installing a windscreen. But if you try pushing into a head-on wind, I'm sure it would take a lot more effort from you.