Honeysuckles are tough plants. It is extremely hard to kill them. The large branches I 'm pretty sure are still alive. If you want to check, you can scrape a bit of the bark off and see if there is still green in them indicating that it is still alive. But if you don't see any sign of life on a branch when other branches are leafing, it is probably dead. You can prune the dead branches anytime. The honeysuckle will recover fully in no time!