The permit is still required, but you are guaranteed to get one. Just stop in at the Visitor Center one mile S of Lone Pine (on the hwy to Death Valley). They might even leave it in the outside drop box if you will be there after hours and call them.
Now... IF there has been a significant snowfall, the road to Whitney Portal will be closed about 3 miles before the Portal. It has always been a "Road Closed" sign that people often drive past. However, if there is snow and ice on the road, you will need the appropriate vehicle, or park and walk in. There is often significant rock debris on the road, too.
I think walking takes about 2 hours. I'd definitely park and walk if there is any storm activity predicted.
