Thanks for the question and pictures.

I strongly suspect that these affected arbor vitae are showing the effects of winter burn. If you did not wrap these trees in the fall, this cause becomes even more probable. During the winter the ground is frozen around the roots so no water can be taken up by the tree. Additionally, winter winds which are low in humidity can draw water out of the needles. During the latter part of January and especially going into February and early March, photosynthesis starts to occur within the needles due to increasing day lengths. Photosynthesis requires water but with no water available to the tree, dehydration occurs within the needles that leads to their browning. The brown areas will not come back. For the tree in your left picture you could remove the browned areas and while the tree might survive, it would be misshapen. For the tree in the right picture where there is a greater degree of browning, you may be better off to replace it. Here is some information on these and other points:

https://hort.extension.wisc.edu/articles/winter-burn/

https://www.lcslawn.com/blog/winter-burn-evergreens/

https://extension.umn.edu/planting-and-growing-guides/protecting-trees-and-shrubs-winter

https://www.mankatofreepress.com/news/local_news/browning-evergreens-may-recover-winter-burn-the-culprit/article_9ee9e3c0-6047-11e8-b435-6b296a01fab8.html

https://www.gardeningknowhow.com/ornamental/trees/arborvitae/winter-damage-to-arborvitae.htm

Good Luck!!