tngirl01 - I don't mean to completely disagree with the previous posters on the driving issue- they are right in that you do want to be cautious and you don't want to assume because Seattle has a temperate climate that driving in winter is a breeze, but it isn't fraught with extreme danger either, and most of us (including teenagers) in the PNW drive throughout the winter without taking our lives in our hands.
I've driven in Portland, Eugene, Spokane (which is less rainy and much more snowy), and Seattle extensively through every season for almost 30 years now, and except for a bizarre day here and there, I've never found driving in the winter here to be particularly hazardous. Of course, I'm not originally from the area, so maybe those who have been born and raised on the west coast and have driven less in other parts of the country would feel differently. I'll admit, Oregonians and Washingtonians are not among the country's best drivers.
Yes, it can get icey (but this isn't a nightly occurence), and yes there can be a lot of water, but they have built many of the roads on the west side so that water runs-off. As long as you remember to pump your brakes slightly after going through an occassional large puddle, and maintain a reasonable speed - it isn't usually a problem.
I've found visibility issues - from fog and driving wind/rain to be a bigger cause for concern, but again, if you are excercising normal safety precautions, it isn't any more hazardous, in my opinion, that the driving obstacles you face in a lot of states and cities in the winter and less than quite a few.
Again, you do want to keep safety in mind, but I don't want you to be terrified to come up here and get behind the wheel either or feel like you can't drive at all 3 months out of the year. Everyone does. The only thing that brings people in Seattle to a screeching halt is 1/2 inch of snow (that's true for the entire west side).
The worst months are December-March, but February for whatever reason seems a little better. However, this can all vary a lot from year to year. The last couple of years, have seemed (to me at least) colder and ranier/icier than usual, but some years are pretty temperate year round. The only thing you can count on is rain.
Driving in an unfamiliar city is scary but part of life. You'll probably start out sticking pretty close to the U-District. Fortunately, most of what you need will be close by, so you won't have much reason to wander far (there is a large mall no more than 5 minutes up the road in addition to the on-campus shopping). As you get comfortable you can wander farther and by then you'll have plenty of friends, I'm sure, from Seattle and surrounding areas who will jump in the car with you and show you where to go.
If it makes you feel any better - some of my best memories are of days I got lost with friends in Seattle.
After a while you'll feel like you know the parts you need to know well.