There aren't really any long trails in the redwood parks, and backpacking is pretty limited there.

Check out the Trinity Alps or Russian Wilderness, although you'll have to deal with snow.

If you're willing to go as far east as I-5 (or a little more) you'll have the Lassen and Shasta options.

Regarding the Lost Coast trail, I'm not sure about rivers but access is limited to some beat up roads that may be impassable in the winter. Winter here is also extremely wet and pretty cold, so I wouldn't recommend hiking along the ocean.