Dear Megan, here's the response to your question:

Hi Megan, thanks for Using Ask Extension

An American Pillar Arborvitae over ten feet tall and well established at five years since planting, should not need to be protected especially if it is not subject to winds and salt. Even with subzero temperatures and windchill temps below –20°F for multiple days can cause minor cosmetic browning, from which established plants can usually recover in spring.  

Your established arborvitae in your sheltered back yard should no longer need winter wrapping. Arctic blasts may cause cosmetic browning, but plants should recover. Focus on soil moisture and mulch prior to winter, not burlap. If you are still concerned, you can place a burlap screen on the windward side rather than wrapping the whole tree. Watering deeply before soil freeze and maintaining 3–4 inches of mulch will help the plants through the winter.  Expect some browning which is recoverable.  

Check out the following links:

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

https://ask.extension.org/kb/faq.php?id=897413

https://extension.psu.edu/preventing-winter-burn-on-evergreen-landscape-plants

I hope this helps.

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