As a former cyclist (amateur bike racer), I want to say that a lot of the cycling clothes we wear are not designed well for running. For instance, when you ride your bike your arms don't swing back and forth -- your top is pretty stationary. I've tried to wear my cycling arm warmers out on a run and it went pretty terribly. Leg warmers obviously won't work at all. The amount of heating we need is also very different, you don't do quite as much work on the bike and the speeds are much higher so the cooling from the wind is a lot higher, so it's really a different thing.
One simple thing that I would do for cycling in the cold was to simply wear two layers. I wore a long sleeve shirt as a base layer (I have a warm synthetic shirt that I like), then put my cycling kit (the normal cycling t-shirt) and my arm warmers over that. Two layers of tight-fititng clothes will block out the wind really effectively and it can help you skip the rain jacket. I also have a couple of rain jackets that I use for easy bike rides, but even though they fit me pretty well they still create too much wind resistance and I hate wearing them on fast rides. When I was racing I only wore them once or twice in longer road races when the weather was so crappy I didn't care about how well I did, and I never wore it in a crit.
Near-freezing rain is truly the worst, I already felt bad for the runners on Thursday when I heard the forecast and didn't know what I'd do in those circumstances -- probably just tempo the race.
Also, while cross country skiers know how to dress for the cold, remember they don't often need to dress for the rain...
Yeah I think XC skiing gear is a better comparative than cycling. Totally different temperature issues for cycling than running. When I first started XC skiing the only extra gear I bought beyond my running clothes was a pair of shell pants to go over my tights. But the exertion level is so similar I rarely wear those. Wet can be a factor (heavy snow fall melting on contact to body) but nothing like yesterday. Bottom line is it’s impossible to prepare for heavy rain in cold. You can only prepare for cold and wind.