Best rain tire = Goodyear Eagle GS-D3
Winter? How? Like just cold or snow and ice too? I'm not really sure what Oregon gets being a coastal state despite being far north.
If you need snow/ice traction, you'll be looking at dedicated winter tires. If you desire good dry road traction too, you'll be looking at performance oriented winter tires. The absolute grip on snow and ice is less then completely dedicated versions, but they'll be a good step up from all-seasons and a BIG step up from any performance tire you can buy. Dry road grip will be around all-season level to mild performance tire level.
Some performance oriented winter tires would be: Bridgestone Blizzak LM-25, Pirelli Sottozero (210 through 270 depending on size), Toyo Garret KX, Dunlop Wintersport 3D, Goodyear UltraGrip GW3, Michelin Pilot Alpine PA3, and others. These types of tires are built like a performance tire, offering a stiffer carcass and better handling but with a tread design that's geared for snow/ice. You get a good mix of properties that make the tires pretty versatile.