Do the deer eat burning bushes and Honeysuckle vines?
Plants Repellent to Deer
First let's clear things up: deer have plants they prefer but if hungry they will eat almost anything. Typically, plants with aromatic leaves are unpleasant to deer. Think Russian sage, lavender, etc. Of the honeysuckle vines, coral honeysuckle, Lonicera sempervirens, is said to be deer resistant. Burning bush, Euonymus alatus, is considered invasive in some locales so check with your state extension service. Rutgers has a rating of how deer-resistant common plants are. Again you might want to check your state's extension service for the deer recommendations in your area. Here is Rutger's list: https://njaes.rutgers.edu/deer-resistant-plants/