If you cut honeysuckle back to control the plant's growth, the best time for pruning is after the plant is done flowering in the summer. This allows the plant to grow healthy stock before the winter weather arrives. Pruning stimulates new growth and if it's done before winter, the new growth may suffer damage from the cold weather. The damage allows pests and diseases to attack the plant, possibly killing the honeysuckle.
Honeysuckle grows similar to grapevines, where the upper portion of the plant is vibrant and full of leaves while the bottom remains bare. Cut the honeysuckle back hard during the dormant part of the growing season to generate new spring growth on the bottom of the plant. Japanese honeysuckle will still bloom during the spring because the blooms grow from the new growth. Dutch honeysuckle produces blooms on the previous season's growth and needs an entire year of growth to produce blooms.
The previous and current season's growth produces the blooms that scent the garden air. Stimulate a bushier plant by pruning the ends of the 1- and 2-year-old vines and removing the old woody vines. Do not cut the vines back too vigorously or the plant will spend most of its energy producing new foliage to replace what you pruned, instead of producing blooms.
Cut back dead and diseased branches and stems before winter to keep pests away and the disease from spreading. Prune any branches that are tangled or growing in an unwanted area. Remove any unwanted shoots growing from the rootstock or underground runners. Prior to winter, mulch the honeysuckle to protect the vine against the cold and to keep in moisture.