Any month you can get on the South Holston is a good month. The best time, in my opinion, for the South Holston is late June and early July. Reason... sulfur hatches. I prefer high water during this time because there's less people and lots of feeding fish. Any other time is good to excellent. I'm a guide up there myself but I've been down in Georgia for the last year helping my mother. If you want a recommendation for a good guide I'd be happy to do so. You'll want a guide that's going to give you more bang for your buck.
Rivers that I like thru Jan-March include the Clinch, South Holston, and Watauga. The Watauga and Clinch will be your best bets for a float because these rivers can be floated on low water. The South Holston is my favorite but you need water to float it or you will need for someone to set up a special trip up for you. Shoot me a PM and let me know what your are looking to get out of your trip. That is the most important thing.