It is the same as the way on a sunny day the sun can heat your car so that it is so hot you can't touch it, though the air temperature may be only 20C or so. Likewise, the entire black night sky is a source of cold (just like the sun is a source of heat) that can cool the ground, or your car, to below the temperature of the air, though the effect is typically not as powerful as for the sun. I think typically your car windscreen frosts over before hoar forms on the grass. One term for this is "radiative frost", as the cold comes from radiation from the sky, as opposed to "convective frost", where the cold is communicated by convection (ie movement) of the air.

Reducing radiative frost is why plants with overhanging evergreen branches can survive the winter much better than those that can "see" the whole black sky. One of the beneficial effects of being against a wall, as opposed to an open situation, is that it reduces the amount of black sky the plant can "see".