Looks like drying from cold. They are not even a year old so water them occasionally, even though cold.

some slight winter damage ... probably related to fall planting ... and perhaps not enough water in your warm zone during winter ...

there may have also been some shipping damage from grower to your house prior to you getting them .... or worse.. if they were sitting in bog box all summer long ...

water deeply and properly.. link below ....letting them near dry in between waterings .. taking into account spring rains ... and when the heat of summer starts building ... the dead stuff can be snipped out ...

its not out of the ordinary ... and if you did a bunch... problems with one or two is within the realm of normal .... if it starts looking real bad.. perhaps it would be worth talking about how you planted them etc ..

its stressed... its not hungry.. fert is not a response ...

ken

https://sites.google.com/site/tnarboretum/Home/planting-a-tree-or-shrub

Ok thanks. I had professionals install them. I have 4 Emerald Green on the backyard west side on the house (no damage).

On the backyard north back side I have 10 Emerald Green arborvitae, 2 are completely orange (dead), the rest have the same orange/white damaged leaves, 5 Green Giant Arborvitae look a bronze color and very thin. The Green Giants was planted by the builder.

Then 4 Emerald Green on the east side. 1 is completely orange (died). The others have the same orange/ white leaf damage. I'm going to have a drip system installed since I don't have irrigation. .

The dead Emerald Green Arborvitae will be replaced.

How should I proceed with the ones with needle damage in addition to watering? Will they die or should I wait until the spring or summer to prune back? Will new buds grow over the damaged needles?

Nothing will come from bare twigs inside the outer shell of foliage. Instead of cutting on them focus on making sure the soil they came in at time of planting is moist all the way through.