Hydrangea arborescens 'Annabelle' flower on new wood, therefore you can safely prune off as much material as you wish in late Winter...
This species blooms on new wood, and may be pruned back close to the ground in late winter each year to revitalize and to encourage vigorous stem growth and best form. Plants may die to the ground in harsh winters. If not pruned back, any weakened and/or damaged stems should be removed in early spring.
The most straightforward hydrangeas to prune are the mostly white flowered, extremely tough and hardy Hydrangea paniculata and Hydrangea arborescens cultivars. H. paniculata cultivars, among others, include 'Brussels Lace,' 'Kyushu,' 'Pee Gee,' 'Pee Wee,' 'Pink Diamond,' 'Unique' and 'White Moth.' H. arborescens cultivars include 'Annabelle' and 'Hills of Snow.' All selections of these two species flower on new wood. Therefore, they can be cut back immediately after flowering and may rebloom (for H. arborescens in long growing seasons) or they can be cut back in the winter and still be expected to flower the following year. How far you cut them back is strictly personal preference. Unless you live in a restricted community with pruning covenants, there are no pruning police. You do not HAVE to prune H. arborescens or H. paniculata at all but it makes for a neater plant and, if you want long stems for fresh or dried flowers, pruning back hard encourages long stems on older plants.