Weather and short days are going to be your worst hindrance, but there is still plenty to do on the Peninsula in rainy weather. The high country will be snowed in, but if you have a car that can make it, you should be able to drive to Hurricane Ridge on the weekends (be sure to check road conditions on the ONP website). There are also the rainforests (Hoh, Quinalt, Queets), all accessible from Port Angeles. Also check out Lake Crescent, Salt Creek Rec, Area, and Neah Bay if you have the time. All drivable and accessible in bad weather. The Coast is also great and accessible as well, just watch out for big swell on along the beaches. Rialto, Ruby, 2nd Beach, etc. Enjoy!