There isn't much info out there. From what I can find on remote snow depth sensors appears to be only a few inches of snow, so I doubt snow shoes would be of much use. Of course, what you may find could be different.
The road certainly has a road closed sign. In the past if that is all there is, people can drive past it, but at their own risk, of course. Not sure if there is a hard-closed gate on the road. It would be great if you could post what you find, both with the gate and the trail conditions.
Be careful, good luck, and have fun!
...and pictures are worth thousands of words.