It really isn't in the rain shadow that Sequim and even up to Mt. Erie enjoy, but it doesn't get near as much rain as the Wet End (West Side).
I have only approached via Mildred (a couple times during that dry winter), but I think that is a nice way to go in, but if you're looking to do more hiking you'll probably want to go in via the other side, unless you just want a quick hike in, a climb or two, and then a hike out.