There are some important factors when deciding to get rid of honeysuckle.
Season
Spring: Not early spring! This will cause honeysuckle to spread rapidly, but late Spring is a OK
Summer: Drought season is the best conditions for using herbicides
Fall: Dry fall weather is a great condition to harvest
Winter: Frozen ground is not good, but wet soil makes for good pulling-from-the-roots conditions
Methods
Controlling Honeysuckle
Diluted Herbicide sprayed directly on the leaves of the targeted plants. Not too wet!
Getting Rid of Honeysuckle
Cutting at the stump and applying herbicide is a very effective method. Apply herbicide directly to cut surfaces (carefully).