I'll second one poster's "layers" idea. Get yourself a good Columbia or North Face waterproof but breathable running jacket, preferably with some fleece inside or Columbia's "Omni-Heat" lining. I ran this evening in the icy rain and wind with my Columbia running jacket. Running tights are great, or get some of the tapered polyurethane running pants that are almost like tights but not so, well, tight. I have both. The reason you want tights or tapered pants in Seattle is that wet weather means wet, heavy pants--the more material you have the heavier it gets. And wet, windy weather just adds to that. Get a good running headlamp because you're going to need it. Wear some reflective gear so drivers can see you from the back. Just common sense, really. In winter, it gets dark a lot earlier in Seattle than it does in San Fran because it's much farther north. Seattle sidewalks and roads are really crappy and uneven, and like one poster said, a lot of the city streets don't have sidewalks. Hell, a lot of the city streets are so narrow, with cars parked on both sides, that two cars can't go down the street at the same side in opposite directions. As someone already mentioned, just east of UW and all around that area there are some really good places to run where the UW XC team trains.
Green Lake is a great place to run, but not on a nice day unless you're just doing an easy recovery run. Too many people on bikes, roller blades, walking with strollers, walking dogs, and just plain crammed together. I think it might be really nice if you go very early in the morning or after dark on a cold, wet Seattle day. But if you don't live near it, don't bother--Seattle traffic sucks, and the crazy thing is, when it rains it doesn't seem like they know how to drive in it. A few drops on the windshield and I-5 becomes a parking lot. Go figure.
Have a positive attitude. You'll need it. Hopefully you're not one of those people who get mood disorders in the winter when you can't get a lot of sunlight. They have special lamps for that disorder, though, and my sister uses one. I've never had a problem with that, but I still hate always having to run in the cold, wet dark except on weekends when I can run in the cold, wet light. But as another poster said, there really aren't any "no go" running days as long as you dress right, wear a light, and don't get uptight. :-)