While minor pruning can be done this time of year (as some people do to obtain pieces of evergreens for holiday decorations), regular or more major pruning on broadleaf evergreens such as yours is best delayed until early spring. It is true that dormant pruning is useful for being better-able to see branch structure, but this is more applicable to deciduous plants rather than evergreens; evergreens can naturally shed some leaves/needles in fall, but it is often not enough to make much of a difference for this application.
There are different pruning techniques depending on the desired outcome. If you need to maintain the shape of your hollies and boxwoods, you can either prune only the errant branch tips or shear them. Be aware, however, that shearing boxwoods (in particular, because their leaves are so small) can promote conditions within the interior of the canopy that are conducive to fungal infection. The poor air circulation that results from a tight, dense outer layer of leaves keeps moisture levels higher for longer, and many fungal organisms remain in an infectious stage for longer in conditions of higher humidity/wetness. It is also prudent to sterilize pruning tools between plants to reduce the risk of them spreading disease. Boxwood Blight, for example, is known to spread via infectious material contaminating pruning tools.
Several pruning styles and general pruning information can be found on this page: https://extension.umd.edu/hgic/topics/pruning-shrubs-and-hedges . You may find that a combination of shearing and heading-back will suffice to maintain manicured shapes - if that is your gardening style - and some thinning pruning will maintain better airflow within the branches to minimize the risk of disease that comes with shearing.