Thanks for your question.

While I don’t doubt that you are seeing something, it is very unlikely that it is a squirrel’s nest. They do not nest in arbor vitae but instead prefer oak and maple trees. Also this is not the time of the year that squirrels build nests. Instead their nesting activities are largely confined to the spring and early summer. What the structure is in your arbor vitae is not clear to me. I did not see any sign of it in the pictures you sent. Maybe it’s an old bird’s nest (robin?)?  Removing this structure will not address your situation. The damage being done to your arbor vitae is most likely due to deer. They just love to nibble on the tips of arbor vitae and are quite messy in their eating habits as evidenced by one of your pictures. Deer also like to strip the bark off of arbor vitae, typically doing so in the longitudinal manner shown in your pictures. The only preventative measure you can take at this point is to wrap the trunks of your arbor vitae with some type of fencing material, preferably of a wire mesh type. This may not prevent them from still eating the branches but your arbor vitae should recover from this. The deer probably now have your arbor vitae on their feeding menu and will most likely continue to visit you for the duration of the winter unless you otherwise deter them.

Good Luck!!