This is a good time to start thinking about what to do in your backyard for birds in the spring.
Instead of 
cleaning it all up, how about thinking differently about that dead wood? About 85 North American birds use dead trees (snags) to nest in – and they aren’t all woodpeckers! Owls, Chickadees, Bluebirds, Nuthatches, American kestrel all like to take over nesting holes in dead trees…as do some ducks. Wait – ducks?? Bufflehead and Wood ducks nest near or over the water in excavated holes from which the babies jump out within the first 24 hours! Most wooded areas are cleared of dead wood, so many of these species find suitable nesting spots hard to come by, and as a result, their numbers are declining. Now you might not have a pond or a forest in your backyard, but that doesn’t mean birds aren’t longing for an occasional pile of limbs or a snag.
Dead trees are also an important source of food for birds as there are a number of beetles and other insects which inhabit them. And a pile of sticks and tree limbs is a source of safety for small birds avoiding a predator, a good place to break the cold winds in winter and small sticks and dead grass can be a source of nesting material. Combine leaving some of this in your yard with native plantings, and you will find your backyard to be a very attractive spot for a greater variety of birds!
Obviously you need to take down trees that pose a safety issue, but if you have any snags that don’t pose a risk, consider keeping them. You might discover that they have nest sites already excavated and you may find there are some active nests. Depending on where you live, some birds may be nesting already, so if you do decide a tree needs to be taken down, check to ensure there are no nesting birds inside it or in its branches. If you don’t have any snags on your property, consider keeping a pile of tree branches near the feeder so birds can escape from a predator attack. Of course, you can always provide bird houses if you don’t have any suitable natural homes. But if you do have the ability to provide natural homes, aka dead trees, take advantage of it and give the birds in your backyard a special treat.