We've done it many times in winter. It's a 5 mile trek, we use cross country skis. You won't be alone especially on weekends.
The road will be closed so it is a longer walk than normal and it isn't uncommon to have 2 or 3 feet of snow on the ground at that time. Also expect snow to fall regardless of weather reports. The mountain range has been know to have it's own weather. You can make it safe but about 7 years ago someone died out there because they slipped and fell and it snowed 12 inches and his friend had to hike out the next morning. That was in march.
Safe? There will likely be snow, so as long as you're good driving and walking in it, then yes.
Thanks! Your answer is awaiting moderation.