I find I cut any time I have the opportunity. Obviously not on a very cold day, but mild winter days are best for me as the other vegetation has not sprouted out yet. (I live in a rural area in the north central part of the state). Be mindful that azaleas need to be pruned right after they bloom to preserve the buds for the next year. If still not sure, research online thru the NC Dept of Agriculture.
You don't. Very few plants, shrubs and trees benefit from pruning in the dead of winter. If done incorrectly, you could even kill your plants.
Contact your local Ag Extension or Master Gardener at a reputable nursery for best local suggestions.
If in Western North Carolina, call B. B. Barnes or Jesse Israel. They can help or point you in the right direction.
wrong time of year, UNLESS, the parts you want to remove are dead stalks from plants (perennials) that regrow in the spring --- but they're not usually referred to as 'trees' or 'bushes' -- SOME hydrangeas will die back and bloom on 'new growth' ... but you need to check 1. your grow zone --- NC runs from the Mountains to the Ocean! and utilize your LOCAL ( County ) Agricultural Agency ---