in Washington, you'll need a m+s rated tire for a mountain run. However you don't need a studded tire. We generally don't have ice unless you live on queen Anne, in which, you stay home. In Seattle, it's not your ability or your car's that is a concern, it's the people in Prius who don't know when to stay off the roads.
I drove my summer tires all last year, winter and summer. You're mostly concerned with having a good rain tire.