I saw Richard P on the other forum posted a picture a week or two ago where he drove over snow all the way up to the Portal.
But that may have been ideal conditions. I wouldn't go over the snow unless I had chains to put on in case I got stuck. And doing that is definitely at your own risk!!!
People have gotten stuck up there in previous years, especially if they drive up there and park, and go on a hike. Then a storm comes and drops enough snow to strand their vehicle.
That being said, if you check the webcam view today, you can see a section of road in the picture, and there is no snow visible in that area. So I'd bet the road is pretty much free of snow well beyond the sign.
