The state park is only car accessable from the Blue Ridge Parkway. Currently the parkway from NC 80 is closed for maintanence on the Twin Tunnels. Only car access is from Asheville. If weather bad or significant icing under one of the tunnels in the Craggies, well........
its a long walk up a big eastern hill. For access see Mitchell state park homepage @ http://www.ils.unc.edu/parkproject/visit/momi/home.html
The summit is closed because of construction of the new tower. Does anybody know how close you can get to the old tower? I think the thought is if you get to the fence, your close enough. I'd park at the park entrance hike out to Commissary Ridge and head up Mt Mitchell trail toward summit. Walk road down to campground and jump on the old Mitchell trail back to office. Ignore the rangers. If they ask you who gave you directions, I don't know nothing!