Sometimes it's better to have a narrow tire to "cut through" the snow. Perhaps the road biker was just better able to penetrate through the fluffy snow to pavement/ice/packed snow.
Studded tires are very helpful in getting grip, but only "adhesive" grip. If the snow was sticking in to your tire and you were throwing a rooster tail of the stuff then studs probably wouldn't have done much good since the problem was "cohesive" grip, or the snow's ability to stay together and not just stick to the tire. If you were sliding around on packed snow or ice then studs would have done wonders, like riding on bare pavement or dirt.