I'll use eggs on rainbows anytime. For browns, though, they really come into their own in early spring with the sucker run, don't really use em over the winter.
Midge dries: I always have a few on me, though I don't use them all that often, and only in situations where fish are showing on the surface. Often, that doesn't seem to start for me until late January through Feb.
The bulk of my winter work is nymphs, deep and rolled slowly on the bottom. Midge pupa, and cressbugs/sowbugs are the standards. Sometimes Hare's Ears and the like.
I also use more streamers in the winter. In the summer, they're pretty much a high muddy water thing, but in the winter I'll use em anytime, fish sometimes suddenly become active when faced with a big baitfish like that.
That said, by late February, I'm using more and more BWO nymphs and watching for the hatches to begin.