I know that area well. I grew up on the Va. side near there. If you can get through the tunnels and to the peak without ice, it should be better temperature wise on the way down. We went up to my uncle's for Christmas once in Bluefield and everything was fine south of the mountain. When we went through the last tunnel and came out it was snow and ice!
The most important thing is to be safe. If you see it is going to get bad don't do it. You might consider going a day early during the warmer times for the mountain.
I found this site.
I don't know how accurate it is.