rabbits have chewed away some bark on many branches of a dogwood clump as well as tree. they didn’t go all the way around but got fairly deep in a few places.
Will pruning paint help these trees or is there a better solution to save them?
I am sorry that your shrubs are suffering from damage from rabbits. There seem to be more and more of them around.
Whether your dogwoods will survive depends on how completely the rabbits have chewed away the bark from main stems or branches. To the extent that they have encircled, or girded a stem, it is unlikely that the the plant will survive, at least above that point, as the cambium will no longer be able to transport water and nutrients up from the roots to the upper parts of the plant and carbohydrates from the leaves to other parts of the plant including the roots.
You indicate that the damage does not go the whole way around the trunk, so there is a possibility that the cambium can continue to do its job. You should be able to tell once the dogwoods start to leaf out in the spring.
If the area above the damage is not healthy, you can prune back to below that point. Dogwood shrubs are quite forgiving and will recover quite well from a hard pruning. Note that if you are fairly certain the the damage is extensive, I suggest that you prune now (late winter/early spring) before they start to leaf out as that is the best to prune dogwoods which flower on new growth. It is also a good time to prune back the damaged branches and twigs.
You did not indicate which kinds of dogwoods you are growing. If you are growing red osiers, or another dogwood, for its coloured branches, you should be giving it a hard prune each year as the the colour is in the new growth.
However, if there is severe damage to a dogwood tree, it is unlikely to survive. Once you are convinced the the tree is severely damaged you could try a hard pruning as there is a possibility that it will generate new growth from suckers around the trunk.
Make sure that your shrubs are well watered and fertilized this year (with compost, or an organic slow release fertilizer). You can also mulch around their base with well composted wood mulch. This will help them conserve water and will slowly break down providing nutrients to your plants.
On a go forward basis you can try and prevent further damage from rabbits by using chicken wire, hardware cloth or tree guards as protection in the winter.
I have attached a link to a previously answered ASK question on rabbit damage which you might find helpful.
https://www.torontomastergardeners.ca/askagardener/rabbits-damage-to-plants/