Red twig dogwood (Cornus alba 'Sibirica') and red osier dogwood (C. stolonifera) bear small white flowers, but unlike their treelike cousin flowering dogwood, they are primarily prized for their colorful red stems. Prune them in late winter or early spring while they are still dormant. First remove any dead or damaged stems.
In addition, remove about a third of the oldest stems annually. The new shoots that sprout from the ground will have a brighter red color in winter. You could also prune them down to the ground annually so they put on all new growth and stay more compact. Depending on their location, red twig dogwoods can grow to be 10 feet tall and 10 feet across.