Seattle is not really a big city, but a bunch of smaller neighborhoods and communities that got grouped together by arbitrary boundaries. Each area has its own smaller culture and scene. Its kinda like Afghanistan, but with aged liberal hippies, yuppie liberal hipsters, and roads that don't blow up when you drive on them. There are lots of hipster douche-bags here. If you can handle them, and the total lack of sunshine, it is not a bad place to be. And traffic sucks. Coffee is great (except for Starbucks, and that Portlandic swill known as Stumptown (which is secretly really good)).
Seattle, and the University of Washington, are significantly more expensive than UofU and SLUT (we do have our own SLUT here too now!). Skiing will be even more expensive out of Seattle. While the season pass might be cheaper, getting there will not be. You are an hour to two hours away from the mountain at Seattle, and we have some of the most expensive gas in the country (said liberals tax the shit out of it). Depending on your vehicle you can spend an excess of $40 a day on gas ($4.25/gal is somewhat standard here). The drivers are also retarded.
I have no idea about UofU, but there is a lack of hot girls on the UW campus (by college standards), and even less warm sunny weather to convince them to take their cloths off on campus (that will be up to you and alcohol, the Sororstitues here do get neked in exchange for alcohol, but that is probably true at UofU too).
The weather is a real issue for many out of state students here (UW). You may not see the sun for three or more months at a time. Most people wright this off, but it can affect you. That said, 20 F is a cold winter day here, and 85 F is a hot summer day, so we do have a very mild climate. Western WA is one of the few places in the world where Nature does not make a constant and active attempt to kill you (Just the dumb Asian drivers).
All that aside:
If skiing is your primary motivation, go to Utah, but don't waste your money on School. You can get drunk and ski for a lot less than instate at either place.