you could need crampons anytime between October and April in the heights. Mt. Mitchell has recorded snowfall in every month of the year. The mountains about 6,000 feet receive fierce weather. I've heard that Mt. LeConte is the coldest place in the south. Snow shoes, you'd probably only need from December until March. Unless you're bushwacking, you'd probably rarely need an iceaxe, maybe just on the Black Mountain Crest Trail or Grandfather Mountain.
When you get above 5,000 feet you start seeing Spruce, Fir and Balsams. When you get above 6,000 you start seeing sub-alpine and alpine conditions. There is some places with arctic tundra above 6500 (Mt. Craig, Mt. Mitchell, Mt. Guyot and Mt. LeConte all have some tundra. Mt. Craig has an awesome open summit with an amazing view.
There are forty southern sixers. I have around 14 of them.
Blacks:
Mitchell
Craig
Balsam Cone
Potato Hill
Winterstar
Gibbs Mtn
Celo Knob
Mt. Hallback
Mt. Gibbs
Blackstock Knob
Smokies:
LeConte
Kephart
Collins
Clingmans Dome
If you do a traverse of the Blacks, start at Bolens Creek on the Black Mtn Crest Trail, hike up to Celo Knob and then camp at Deep Gap (really nice campspot, but it gets windy and cold) and then take the BMCT to Mitchell. That will get you Celo Knob, Gibbs Mtn, Winterstar, Potato Hill, Balsam Cone, Craig and Mitchell. From there take the Mitchell trail to Steppes Gap and bushwack up to Mt. Hallback. From Steppes Gap bushwack up the ridge to Mt. Gibbs, over the lesser peaks of Clingmans Peak and Potato Knob (amazing 360* view) and then bushwack to the Mountains to Sea Trail and climb up to Blackstock Knob, the sothern most peak of the blacks. Then drop down into Balsam Gap and then hike up to Craggy Dome, which is not one of the Blacks, but is not far from the Blacks and is another one of the sixers.
That would be an awesome Traverse. Hiking the Blacks is amazing. It's definately one of my favorite hikes anywhere. I love the views. You're so high above everything.
Mt. Mitchell is kind of touresty, it has a restaurant, museum, observation tower, snackshop and road leading up to it. But, the restaurant has good food and is a good place to eat lunch while in the midst of a tough hike.
Climbing up to Celo Knob from Bolens Creek is a long tough grind that climbs around 3600 feet. You have to bushwack to Celo Knob and Gibbs Mountain from the BMCT. The openess of the ridge line is really cool. If you manage to get good weather, which is a rarety in those mountains, the views are amazing. The trees are very mangled, stunted and sparse up on the ridge. The trail doesn't get much maintenance since it's so high up and far from roads, so it's almost a bushwack itself, once you're south of Deep Gap, the trail recvs more traffic. Most people only hike from Mitchell to Mt. Craig.
this is a cool picture of the Black Mountain Range