You need to have better drainage to allow the water to run OFF the road bed. Then it is just a matter of shoving the snow off the road. You need a swale along each side of the road to allow the water a place to go. And you need to plow the snow far enough to the side to allow room for the water to run off the road bed.
If you notice how the state plows the highways, they don't just plow the road surface. They plow back several more feet to allow the melt to go somewhere. you have to do the same.