It’s a good idea to prune your shrubs and trees now, while they are dormant (not the late-spring-flowering ones, like Buddleia and Crepe Myrtle; check with your neighborhood nursery). Dormancy makes trees and shrubs less likely to sustain damage from pruning. And there is one other big reason to prune now: winter weather is exceedingly dry and the likelihood of fire is high. Pruning branches away from the house is a sensible way to keep sparks from igniting it.
I prefer to trim small trees and large-bush branches with a handsaw. If you make a ” / ” notch on the underside of the branch halfway through it, then saw down straight through the notch from the top, it falls away like a lumberjack cut it. The closer to the trunk of the tree you cut, the healthier it is for the tree and the easier it is for you.
As for shrubs, trim them to their natural shapes. I have a neighbor who cuts his rosebushes with a chainsaw into upside-down pyramids and they only flower on top now. The flat tops shade the bottom branches so the bottom gets no sun. He asked me why the roses don’t bloom all over and I said, “Because they’re scared.”
But enough about chainsaw massacres. Prune lightly all over, especially on the side next to the house, to lower the risk of fire spreading to the structure. It also lowers the risk of your cat climbing up abutting branches and getting stuck on the roof. Don’t ask me how I know.