Rabbits are a huge pest and hopefully fox and birds of prey will reduce their numbers. The only thing that works is fencing until the shrubs are well established and if the winter has a lot of snow cover they can still prune shrubs off that the snow line. Rabbits don’t eat yew or juniper or cedar. Some years they give my barberries a hard prune and other years the forsythia.  Same for dogwood. Those shrubs grow back and look fine by summer. They also leave mock orange and cotinus alone. 
Plastic fencing and bird netting will keep them away and is inexpensive and easy to remove in the spring. Rabbit fencing that is metal is expensive and for year round. I have to keep my blueberries fenced.

https://yardandgarden.extension.iastate.edu/how-to/susceptibility-plants-rabbit-damage#seldomwoody

https://extension.psu.edu/programs/master-gardener/counties/pike/publications/rabbit-resistant-garden-and-landscape-plants

https://www.gertens.com/blog/deer-and-rabbit-resistant-plants.html

https://northerngardener.org/battling-bunnies-garden/

https://www.extension.iastate.edu/smallfarms/protecting-trees-and-shrubs-against-rabbits-winter