We are seeing the effects of November's frost in many of the plants in our landscapes. Your honeysuckle may be one of these plants.
Don't give up just yet, it may take additional time for growth to begin. You can bend the vine and see if it "snaps"' it may be dead and you can prune the area back until you find live tissue. You can also leave it and wait to see if new growth appears.
As we Colorado gardeners know, our weather and seasons are variable; each year presents itself differently.