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The coast that time of year will be generally hit or miss, but you're about as likely to have decent conditions as you are to have crappy conditions. There's a better chance of better weather the further south you go, so the very southern stretch of Oregon is most likely going to give you better results than the Olympic coast. That said, places like Ruby, Second and Rialto Beach work just fine even if it's overcast and / or foggy.
As for the mountains, you'll find snow, snow and more snow. Expect to find 15-20 feet of it on the ground at both Crater Lake and Mount Rainier (the rim drive at Crater Lake will be closed, and with the exception of the road between Longmire and Paradise so will all the roads at Rainier). Likewise up at Hurricane Ridge in Olympic National Park, but there should be considerably less snow there and the road is plowed and open on the weekends over the winter (weather permitting) so you very well might be able to make it up there (you are required to carry chains until April 1). March and April is still early for the valleys to melt out too, so even in places like Sol Duc and the Hoh there very easily could be snow on the ground. Things will still be pretty brown that time of year in the forests too, so focusing on areas which aren't dominated by undergrowth will likely provide better opportunities - there are some good forests around Lake Crescent, the Elwha valley and Quinault, but the Hoh is a bit ugly that time of year in my experience.
Don's suggestion of both the Columbia Gorge and Silver Falls State Park are good - but again there won't be much in the way of ripe foliage yet. You might be able to find some early flowers in the eastern side of the Columbia Gorge by early April (the Balsam usually starts blooming by mid April), and the Palouse is another good suggestion, as the weather over on that side of the mountains will be considerably better.