The job is best done in late winter or early spring.
In thinning out flowering trees, you'll be removing branches that are alive and disease-free, but ill-positioned or otherwise undesirable. For instance, you shouldn't have any two branches of your flowering trees coming into contact with each other. Such contact invites disease; and an overly thick canopy casts too much shade on the flowering tree's lower branches.
True, pruning off such branches in late winter or early spring may lessen the impact of a flowering tree's floral display for that year. But in the long run, the pruning will be beneficial.
The next FAQ addresses the question of when to prune evergreen trees.