Good Morning Tiffiny, 

Thank you for contacting the U of M Extension Service. 

From your photo, I cannot tell where the arborvitae are located. My first thought is that the damage could be from snow with deicing salt in it. This would damage the vegetation on the plants. Please click on this link from the U of M Extension Yard and Garden website about deicing salt: https://extension.umn.edu/lawns-and-landscapes/effects-deicing-salts-landscapes.  

We've had a long cold winter. Was snow piled up around the trees? Also, the damage could be caused by drought damage. We had a very dry summer last year. Did you water the shrubs in the fall? 

Here is a link from the Missouri Botanical Garden about a blight that is possible in arborvitae: https://www.missouribotanicalgarden.org/gardens-gardening/your-garden/help-for-the-home-gardener/advice-tips-resources/pests-and-problems/diseases/needlecasts/pestalotiopsis-tip

These branches will not sprout new growth. Here is a link about protecting trees and shrubs in winter: https://extension.umn.edu/planting-and-growing-guides/protecting-trees-and-shrubs-winter

Good Luck!