When examining the leafless canopy, look for broken, damaged and dead branches, decay cavities, rubbing and crossing branches, and weakly attached branches that form a "V" type union. It might seem difficult at first, but soon you will begin to see branches that don't have buds or the bark is sloughing off, which are pretty good signs that the branch is dead. Following some of the recent storms, including hurricane Sandy, there might be broken branches that are still hanging in the tree that should be removed before they fall out and cause damage. Look for splits or cracks in branches and cavities in the trunk or large branches.
Co-dominant stems are formed when two branches that are about the same diameter come together to form a tight V shaped union. Over time these two stems will get larger in diameter, applying pressure to each other until one stem breaks out, usually in a storm or high wind event. These tight V unions are not as strong as smaller branches that are attached with something called a branch collar. These branches tend to be growing at a 45 degree angle to the trunk and are tightly held in place by branch collars, formed by trunk wood. It is best to remove one of the co-dominant stems when the tree is young or the branch is small.
Once you evaluated your trees in the winter, you might decide they need to be pruned, either by a professional arborist or yourself, as long as you can do that safely (never climb a tree unless you have been trained to do this work and are using ropes and safety equipment). Winter is a good time to prune because we can see branch structure, insects and diseases are not present, and the tree will devote some of its stored energy into closing the pruning wounds in the spring as it begins to grow. Some worry about species that "bleed" when pruned in the winter, but it is only sap flowing from species such as maple, birch, beech and elm and it does not harm the tree.
Winter is also a good time to have an arborist evaluate and prune your trees because it is their slower season. Who knows, you might even get a better price during the winter months. Just make sure you find someone who is knowledgeable, like an ISA Certified Arborist, and will not "top", "over thin", or damage your tree.