I have had similar rabbit damage to our blueberry shrubs. If the soil pH is right, and if the shrub is kept watered, it will recover to some extent. You might want to give it an ounce of water soluble fertilizer, once a month, in May and June. I have used Plantskydd spray repellent with limited success. It works best if the rabbits have an alternate source of food, something like the cup of corn I put out every evening, just before bed. There is not much for a rabbit to eat when snow covers everything. Once the world turns green, the pressure is off the shrubs.

Should I cut off the dead branches?

Bump! Please, experts! I need some direction before I proceed! I'd hate to make this worse, altho it's hard to imagine these looking any uglier.

My suggestion is to allow the shrub to green up this spring, and then decide what to prune away. The delay will give you a chance to see what is really dead. Do you know the pH of the soil? If the pH is in the right range, the shrub will recover more quickly, and fill in the empty space with new growth.

Do not follow the advice to use water soluble fertilizer. It is more of a problem than a solution. A good rhododendron fertilizer has organic nitrogen to prevent harming the mycorrhizae in the soil which is important for rhododendrons and azaleas. One such fertilizer is HollyTone. If you use that apply once, now, and only apply at half of the rate on the package.

Rabbits will eat almost anything and will bite into anything, even a garden hose.

Thanks. This helps!

I'm really happy to report that there is new growth coming along the previously chewed sections! It'll probably take quite some time to fill out, but at this point I'm overjoyed to see some life on the savaged appendages!