Water temperature is the big thing to pay attention to for winter fishing. You want to find the warmest water you can because that's where the trout will tend to be & where they'll be feeding -if they're feeding at all. As the water temps drop so does a trout's metabolism until it gets so cold they are essentially in a trance.
Spring fed streams & tail waters below dams are your best bets. If you're stuck with only freestone streams look for places where springs run into the creek - or where "feeder" streams dump in. At those places there will at least be moving water that will help slow down the formation of surface ice. With spring water coming out of the ground at a consistent temperature, it's a good bet fish will be found just down stream of where the spring enters the stream.
You're going to want to fish in the warmest time of the day, too. This isn't just for your comfort, but also because early in the morning the water temps are their coldest. So sleep late & show up in the middle of the day.
As I said before, trout physically slow down in winter. They won't move around a lot for food. Usually the places they have chosen for cover in winter will also have a food supply - & they won't be eating as much either. You want to find these places where the trout are & practically hit them on the nose with your fly to get them to strike. The ideal place would be something like a deeper pool with slower water that has some natural cover, just below a point where a large spring enters the stream.
Winter's not the time to be covering a lot of water. You want to study the stream to find the places where the trout are at. Once you find them, fish them thoroughly & keep going back to them on every winter trip, as the fish won't be moving around to different locations much, if at all.
Because the trout aren't very active, you're going to have to slow your fly down in the drift. Attractor nymphs, egg patterns, & even streamers swung in a dead drift may do the trick, but you'll have to get them down deep to the level where the fish are. Fish slowly & deliberately moving your fly only a foot or two to the left or right on each cast. Remember that you have to practically hit the trout with your fly. Be patient & methodical. Slow your fly down by mending line properly to do so & add weight to your leader as necessary.
Enough can't be said about safety while fishing in the winter. It's always a good idea to have someone along with you & to stay withing eye & ear shot of each other. Hypothermia is no joke. Even if you're the best Olympic swimmer in the world, if you take a dunk in winter you're in big trouble & you'll have only a few short minuets before the worst could happen.
Be aware of ice both in & around the water. High water in winter carries large, heavy chunks of ice that are moving way too fast for you to dodge when wading. It's a good idea to stay out of the water all together. Beware of iced-over banks, too. You might think what you're standing on is earthen shore when it might actually be ice. Never stand on ice along the stream bank. You don't know what's under there & if it breaks away under your weight you're going to be in trouble.
One tackle tip for you lovers of bamboo fly rods: I have a general rule for myself that says "if it's below freezing outside, or if it's cold enough for ice to form in the line guides, I leave my bamboo rod at home". The cold can make the glue holding the rod joints together brittle & even a little stress could cause breakage in the rod - especially in the tip section where there isn't a lot of bamboo. Rather than face the heartbreak of a damaged rod, fish with your favorite fiberglass or graphite fly rod when it's that cold outside.
Cabin fever may be getting the best of you. Maybe you just can't wait until spring to wet a line? So why not go out there in the cold & snow? Winter fly fishing can be really fun. With a little planing, patience, & an eye toward safety you might enjoy some tight lines before the Spring gets here!!!