IMO, you may still struggle to catch fish in the Winter with a dry dropper, despite the above good advice. Unless you’re on a fairly small “Brookie” type stream, it’s hard to get the dropper deep enough most of the time. Fish are almost always glued to the bottom in Winter. I don’t really like fishing a dropper much longer than about 24” or so, and in the warmer months I prefer to fish a dropper at about 12” off the dry. Becomes a pain to cast the longer the dropper is, and the dropper weight becomes an issue. If you go with a heavy, tungsten type fly to get it down quick, you’ll need a really, really buoyant dry to float it. You’re probably talking like a big foam hopper. If you go with a lighter nymph, you can get away with a more natural dry, but you’re gonna struggle to get that nymph down to the fish at all.
I’ve had decent dry/dropper fishing as early as early April, and I can usually count on a dry/dropper working pretty well until the spawn in the Fall or so. But from the spawn, until the water warms closer to 50 or so again in the Spring, I think a traditional indicator rig, that can support more weight to get the flies down, or, a Euro approach will work better. (Again, outside of small Brookie streams. Dry/dropper will still work decent in Winter on those.)
I’ve seen guys trying to fish like a 4 or 5 ft dropper off a dry fly sometimes. IMO, you’re just nymphing at that point and an indicator or Euro approach will be more effective and easier to work with.