Squirrels Eating My Arborvitae . Squirrels continue to build nests in my tall arborvitae trees leaving openings in the foliage, which is unattractive. I hope you can offer insight please. Pine Tree Clusters of Needles Falling Off Walter Reeves The from www.walterreeves.com Work in sections and try to remove all of them. Rabbits and deer like to eat the shoot or new growth on arborvitae. Of course, squirrels are often the beneficiary of suet, seeds and peanuts i provide the birds.