Go for it. It is a beautiful wild place, in your face with wind, the sound of crashing waves, salt on your lips, rock reefs to explore, sea mammals, eagles, ravens, and LOTS of raccoons.
I've gone out to Cape Alava in February, between storms. it was wet and windy, but the eagles flew right over our heads. The hike to the beach is just 3 miles and easy, but if the board trails are frosty, you can go down fast.
Bears are possible, but raccoons are guaranteed. The park requires a bear can and you will want one. They loan them out at the Port Angeles ranger station--- I don't know about winter. At Cape Alava I had a raccoon try to steal my gorp in broad daylight while I was leaned up against a tree and reading. They woke us up screaming and fighting close by and night. The ravens can open a pack zipper, and will.
We did a hike to Rialto Beach at high tide and we had to walk on the disk-shaped cobbles just down from the driftwood line. They were like ball bearings, allowing you to take one step forward and sliding half a step back. It was the toughest flat hike ever. The odd movements used some unpracticed muscles and made me sore. Lower tide leaves hard packed sand better than a city sidewalk and with fewer obstacles.
We should be getting some weird stuff coming ashore from the Japan tsunami.
Like I said, watch your aluminum poles.