I've only been over Anderson in August, switchbacking up dry trail. The pass itself isn't that impressive, just a low saddle and still in the trees. You might have to pay close attention to route-finding. I don't do much winter hiking over passes like that, but I would think the above advice on ice axe and at least some traction device is good.
Also, keep in mind that no trail maintenance will have been done yet. I don't know about the EV b/c I came at Anderson from O'Neil Pass, but the Dosewallips valley will probably have a lot of blown-down trees, especially around Diamond Mdw and Big Timber camps. The Dosewallips river can be tough to cross in a few areas too. As a half-way exit point, just note there won't be anyone at Dosewallips Ranger Station and the road is still washed out between 5-8 (can't remember) miles down the road. No big deal, just a long road walk.
I also think the going will be tough from Bear Camp up and over Hayden Pass.
May might make this a difficult trip, but I think Olympic is absolutely amazing!
Edit: not sure what the requirements are for that time of year, but I think bear canisters are now required for ONP.