Oh, yeah, you can do it. The question is how much discomfort are you comfortable with? The southern part of the route could be very nice, but WA and OR? Oy. I saw a blog of a Norwegian riding across CANADA in the winter, so anything is possible. As a challenging lark? Go for it, but avoid all natural fibers. Make sure you've got totally waterproof panniers like Ortliebs or something similar with roll-top closures. Definitely get a synthetic sleeping bag, and be okay with riding in, setting up and taking down camp in the rain. Truly stormy conditions will likely necessitate lay-overs. Being on the road with traffic in pouring rain and high winds is not recommended.
If having fun is more important, go later in the year. To avoid traffic, skip the Oregon coast and take the Willamette valley through Eugene and such. Lots of nice, lightly traveled roads through there, although getting back to the coast is a little tricky. A good study of maps should help. I suggest taking a short stretch of I 5 from OR to CA then, at Yreka, riding along the Klamath River and out to the coast that way. Check it out. Some awesome country in there. I wouldn't do it in Feb., however. Too much snow likely.
If you want to do a long tour at that time of year, why not the Southern Tier? That's a perfect time to start! Warm desert in the spring--sweet!