I have been keeping tabs on winter fishing and on fishing the Davidson River as well, and I recently did a stream report on the Davidson as well. So, when I learned about the big browns that were caught in the Davidson in late December 09, I had an interview with Ralph McClellan Jr. of Mountain Fly Fishing Adventures who has guided on the Davidson for many years. Ralph points out that the Davidson is one of the best rivers east of the Mississippi River and as such gets a good deal of pressure.
Although you may be after some of the trophy trout population in the 16" to 24" sizes, think small in the area of size #20 through #24. Remember that these trout have seen a good many imitation flies in their life so the stream may present a technical challenge according to Ralph. Try using midges or try to match some of the naturals that you see in red, black, gray and cream colors.
Fish the lightest and longest leader that you can be comfortable with, perhaps a 7x leader. Use a longer rod, especially in the lower portion as it will allow you to achieve a drag free drift and you will get longer casts in the open runs. Ralph willl sometimes use a 4 WT rod, but he prefers the heavier 5 WT or 6WT rods. The weight of the rod will permit you to land the larger trout.