There are bits of the rainforest that you can probably get into at quinault,WA. Not sure but I think it's a town inside a National Forest. I don't think that they can block you from driving in there. I seem to remember a beautiful view of the lake from a campground. If the campground is USFS, it will be closed but there are private lodges in there, I think.
La Push is sorta straight west of Forks, WA and I've heard the hiking along the shore is quite nice. I've not been there. It's on my list though. It's on Indian Reservation so it should not be closed.
If you are heading into Oregon, one state park that is really pretty special is Silver Falls State Park. It really could be a National Park someday. It's that special. Lots of steps going down from the parking lot to get to the bottom of the water falls (no matter which end you start from) but there are 10 large waterfalls along the hike. Two of which you get to walk behind the falls to continue on the trail. I don't remember if you said how old your kids are but if they can totally listen to your command of WALK and are not afraid of taking a five to 10 mile hike... it's something to look into doing. If you have 8, 10 and 12 year olds, they are going to love this hike. If you have 8, 6, and 4 year olds... skip it. Mostly paved steps and paved trails but not pet friendly at all. I don't think it's allowed to take dogs on the trail. No Potty stops along the trail either. Those are at the parking areas.
If you toughed out that stormy weather in a camper... you are a bunch of troopers!! I hope you are able to get out and enjoy the weather now.
As far as Grant's Pass... there are actually 7 low elevation passes (all below 5,000 feet. Most are around 3,000 ft elevation.) It's very seldom that they get snow that sticks on the road until late November. Fog isn't fun either so it's not just snow that will make driving less fun. There's weather cams that let you see what's happening in real time.
Oregon TRIP CHECKhttp://tripcheck.com/Pages/RCMap.asp?mainNav=RoadConditions&curRegion=7