I personally find clothing requirements quite different for running compared to cycling. You warm up quicker whilst running, and at the same time there's less bite from wind chill. So all in all you can get away with fewer layers, and I wouldn't bother at all with trying to be waterproofed when running, maybe just a light, wind-resistant shell over a couple of layers. I get wet from sweat anyway, but the wetness doesn't chill you to the bone like it does when cycling.
I personally find clothing requirements quite different for running compared to cycling. You warm up quicker whilst running, and at the same time there's less bite from wind chill. So all in all you can get away with fewer layers, and I wouldn't bother at all with trying to be waterproofed when running, maybe just a light, wind-resistant shell over a couple of layers. I get wet from sweat anyway, but the wetness doesn't chill you to the bone like it does when cycling.